#include <bits/stdc++.h>
using namespace std;

#if (defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && \
     __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__)
#define ABSL_IS_LITTLE_ENDIAN 1
#elif defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__) && \
    __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
#define ABSL_IS_BIG_ENDIAN 1
#elif defined(_WIN32)
#define ABSL_IS_LITTLE_ENDIAN 1
#else
#error "absl endian detection needs to be set up for your compiler"
#endif

namespace absl {

namespace int128_internal {

// Casts from unsigned to signed while preserving the underlying binary
// representation.
constexpr int64_t BitCastToSigned(uint64_t v) {
  // Casting an unsigned integer to a signed integer of the same
  // width is implementation defined behavior if the source value would not fit
  // in the destination type. We step around it with a roundtrip bitwise not
  // operation to make sure this function remains constexpr. Clang, GCC, and
  // MSVC optimize this to a no-op on x86-64.
  return v & (uint64_t{1} << 63) ? ~static_cast<int64_t>(~v)
                                 : static_cast<int64_t>(v);
}

}  // namespace int128_internal

class int128;

class uint128 {
 public:
  uint128() = default;

  // Constructors from arithmetic types
  constexpr uint128(int v);                 // NOLINT(runtime/explicit)
  constexpr uint128(unsigned int v);        // NOLINT(runtime/explicit)
  constexpr uint128(long v);                // NOLINT(runtime/int)
  constexpr uint128(unsigned long v);       // NOLINT(runtime/int)
  constexpr uint128(long long v);           // NOLINT(runtime/int)
  constexpr uint128(unsigned long long v);  // NOLINT(runtime/int)         
  constexpr uint128(int128 v);             // NOLINT(runtime/explicit)
  explicit uint128(float v);
  explicit uint128(double v);
  explicit uint128(long double v);

  // Assignment operators from arithmetic types
  uint128& operator=(int v);
  uint128& operator=(unsigned int v);
  uint128& operator=(long v);                // NOLINT(runtime/int)
  uint128& operator=(unsigned long v);       // NOLINT(runtime/int)
  uint128& operator=(long long v);           // NOLINT(runtime/int)
  uint128& operator=(unsigned long long v);  // NOLINT(runtime/int)
  uint128& operator=(int128 v);

  // Conversion operators to other arithmetic types
  constexpr explicit operator bool() const;
  constexpr explicit operator char() const;
  constexpr explicit operator signed char() const;
  constexpr explicit operator unsigned char() const;
  constexpr explicit operator char16_t() const;
  constexpr explicit operator char32_t() const;
  constexpr explicit operator short() const;  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned short() const;
  constexpr explicit operator int() const;
  constexpr explicit operator unsigned int() const;
  constexpr explicit operator long() const;  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned long() const;
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator long long() const;
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned long long() const;
  explicit operator float() const;
  explicit operator double() const;
  explicit operator long double() const;

  // Trivial copy constructor, assignment operator and destructor.

  // Arithmetic operators.
  uint128& operator+=(uint128 other);
  uint128& operator-=(uint128 other);
  uint128& operator*=(uint128 other);
  // Long division/modulo for uint128.
  uint128& operator/=(uint128 other);
  uint128& operator%=(uint128 other);
  uint128 operator++(int);
  uint128 operator--(int);
  uint128& operator<<=(int);
  uint128& operator>>=(int);
  uint128& operator&=(uint128 other);
  uint128& operator|=(uint128 other);
  uint128& operator^=(uint128 other);
  uint128& operator++();
  uint128& operator--();

  // Uint128Low64()
  //
  // Returns the lower 64-bit value of a `uint128` value.
  friend constexpr uint64_t Uint128Low64(uint128 v);

  // Uint128High64()
  //
  // Returns the higher 64-bit value of a `uint128` value.
  friend constexpr uint64_t Uint128High64(uint128 v);

  // MakeUInt128()
  //
  // Constructs a `uint128` numeric value from two 64-bit unsigned integers.
  // Note that this factory function is the only way to construct a `uint128`
  // from integer values greater than 2^64.
  //
  // Example:
  //
  //   absl::uint128 big = absl::MakeUint128(1, 0);
  friend constexpr uint128 MakeUint128(uint64_t high, uint64_t low);

  // Uint128Max()
  //
  // Returns the highest value for a 128-bit unsigned integer.
  friend constexpr uint128 Uint128Max();

  // Support for absl::Hash.
  template <typename H>
  friend H AbslHashValue(H h, uint128 v) {
    return H::combine(std::move(h), Uint128High64(v), Uint128Low64(v));
  }

  // Support for absl::StrCat() etc.
  template <typename Sink>
  friend void AbslStringify(Sink& sink, uint128 v) {
    sink.Append(v.ToString());
  }

 private:
  constexpr uint128(uint64_t high, uint64_t low);

  std::string ToString() const;

  // TODO(strel) Update implementation to use __int128 once all users of
  // uint128 are fixed to not depend on alignof(uint128) == 8. Also add
  // alignas(16) to class definition to keep alignment consistent across
  // platforms.
#if defined(ABSL_IS_LITTLE_ENDIAN)
  uint64_t lo_;
  uint64_t hi_;
#elif defined(ABSL_IS_BIG_ENDIAN)
  uint64_t hi_;
  uint64_t lo_;
#else  // byte order
#error "Unsupported byte order: must be little-endian or big-endian."
#endif  // byte order
}; //uint128

// allow uint128 to be logged
std::ostream& operator<<(std::ostream& os, uint128 v);

// TODO(strel) add operator>>(std::istream&, uint128)

constexpr uint128 Uint128Max() {
  return uint128((std::numeric_limits<uint64_t>::max)(),
                 (std::numeric_limits<uint64_t>::max)());
}

//int128
class int128 {
 public:
  int128() = default;

  // Constructors from arithmetic types
  constexpr int128(int v);                 // NOLINT(runtime/explicit)
  constexpr int128(unsigned int v);        // NOLINT(runtime/explicit)
  constexpr int128(long v);                // NOLINT(runtime/int)
  constexpr int128(unsigned long v);       // NOLINT(runtime/int)
  constexpr int128(long long v);           // NOLINT(runtime/int)
  constexpr int128(unsigned long long v);  // NOLINT(runtime/int)
  constexpr explicit int128(uint128 v);
  explicit int128(float v);
  explicit int128(double v);
  explicit int128(long double v);

  // Assignment operators from arithmetic types
  int128& operator=(int v);
  int128& operator=(unsigned int v);
  int128& operator=(long v);                // NOLINT(runtime/int)
  int128& operator=(unsigned long v);       // NOLINT(runtime/int)
  int128& operator=(long long v);           // NOLINT(runtime/int)
  int128& operator=(unsigned long long v);  // NOLINT(runtime/int)

  // Conversion operators to other arithmetic types
  constexpr explicit operator bool() const;
  constexpr explicit operator char() const;
  constexpr explicit operator signed char() const;
  constexpr explicit operator unsigned char() const;
  constexpr explicit operator char16_t() const;
  constexpr explicit operator char32_t() const;
  constexpr explicit operator short() const;  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned short() const;
  constexpr explicit operator int() const;
  constexpr explicit operator unsigned int() const;
  constexpr explicit operator long() const;  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned long() const;
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator long long() const;
  // NOLINTNEXTLINE(runtime/int)
  constexpr explicit operator unsigned long long() const;
  explicit operator float() const;
  explicit operator double() const;
  explicit operator long double() const;

  // Trivial copy constructor, assignment operator and destructor.

  // Arithmetic operators
  int128& operator+=(int128 other);
  int128& operator-=(int128 other);
  int128& operator*=(int128 other);
  int128& operator/=(int128 other);
  int128& operator%=(int128 other);
  int128 operator++(int);  // postfix increment: i++
  int128 operator--(int);  // postfix decrement: i--
  int128& operator++();    // prefix increment:  ++i
  int128& operator--();    // prefix decrement:  --i
  int128& operator&=(int128 other);
  int128& operator|=(int128 other);
  int128& operator^=(int128 other);
  int128& operator<<=(int amount);
  int128& operator>>=(int amount);

  // Int128Low64()
  //
  // Returns the lower 64-bit value of a `int128` value.
  friend constexpr uint64_t Int128Low64(int128 v);

  // Int128High64()
  //
  // Returns the higher 64-bit value of a `int128` value.
  friend constexpr int64_t Int128High64(int128 v);

  // MakeInt128()
  //
  // Constructs a `int128` numeric value from two 64-bit integers. Note that
  // signedness is conveyed in the upper `high` value.
  //
  //   (absl::int128(1) << 64) * high + low
  //
  // Note that this factory function is the only way to construct a `int128`
  // from integer values greater than 2^64 or less than -2^64.
  //
  // Example:
  //
  //   absl::int128 big = absl::MakeInt128(1, 0);
  //   absl::int128 big_n = absl::MakeInt128(-1, 0);
  friend constexpr int128 MakeInt128(int64_t high, uint64_t low);

  // Int128Max()
  //
  // Returns the maximum value for a 128-bit signed integer.
  friend constexpr int128 Int128Max();

  // Int128Min()
  //
  // Returns the minimum value for a 128-bit signed integer.
  friend constexpr int128 Int128Min();

  // Support for absl::Hash.
  template <typename H>
  friend H AbslHashValue(H h, int128 v) {
    return H::combine(std::move(h), Int128High64(v), Int128Low64(v));
  }

  // Support for absl::StrCat() etc.
  template <typename Sink>
  friend void AbslStringify(Sink& sink, int128 v) {
    sink.Append(v.ToString());
  }

 private:
  constexpr int128(int64_t high, uint64_t low);

  std::string ToString() const;

#if defined(ABSL_IS_LITTLE_ENDIAN)
  uint64_t lo_;
  int64_t hi_;
#elif defined(ABSL_IS_BIG_ENDIAN)
  int64_t hi_;
  uint64_t lo_;
#else  // byte order
#error "Unsupported byte order: must be little-endian or big-endian."
#endif  // byte order
};

std::ostream& operator<<(std::ostream& os, int128 v);

// TODO(absl-team) add operator>>(std::istream&, int128)

constexpr int128 Int128Max() {
  return int128((std::numeric_limits<int64_t>::max)(),
                (std::numeric_limits<uint64_t>::max)());
}

constexpr int128 Int128Min() {
  return int128((std::numeric_limits<int64_t>::min)(), 0);
}

// --------------------------------------------------------------------------
//                      Implementation details follow
// --------------------------------------------------------------------------

constexpr uint128 MakeUint128(uint64_t high, uint64_t low) {
  return uint128(high, low);
}

// Assignment from integer types.

inline uint128& uint128::operator=(int v) { return *this = uint128(v); }

inline uint128& uint128::operator=(unsigned int v) {
  return *this = uint128(v);
}

inline uint128& uint128::operator=(long v) {  // NOLINT(runtime/int)
  return *this = uint128(v);
}

// NOLINTNEXTLINE(runtime/int)
inline uint128& uint128::operator=(unsigned long v) {
  return *this = uint128(v);
}

// NOLINTNEXTLINE(runtime/int)
inline uint128& uint128::operator=(long long v) { return *this = uint128(v); }

// NOLINTNEXTLINE(runtime/int)
inline uint128& uint128::operator=(unsigned long long v) {
  return *this = uint128(v);
}

inline uint128& uint128::operator=(int128 v) { return *this = uint128(v); }

// Arithmetic operators.

constexpr uint128 operator<<(uint128 lhs, int amount);
constexpr uint128 operator>>(uint128 lhs, int amount);
constexpr uint128 operator+(uint128 lhs, uint128 rhs);
constexpr uint128 operator-(uint128 lhs, uint128 rhs);
uint128 operator*(uint128 lhs, uint128 rhs);
uint128 operator/(uint128 lhs, uint128 rhs);
uint128 operator%(uint128 lhs, uint128 rhs);

inline uint128& uint128::operator<<=(int amount) {
  *this = *this << amount;
  return *this;
}

inline uint128& uint128::operator>>=(int amount) {
  *this = *this >> amount;
  return *this;
}

inline uint128& uint128::operator+=(uint128 other) {
  *this = *this + other;
  return *this;
}

inline uint128& uint128::operator-=(uint128 other) {
  *this = *this - other;
  return *this;
}

inline uint128& uint128::operator*=(uint128 other) {
  *this = *this * other;
  return *this;
}

inline uint128& uint128::operator/=(uint128 other) {
  *this = *this / other;
  return *this;
}

inline uint128& uint128::operator%=(uint128 other) {
  *this = *this % other;
  return *this;
}

constexpr uint64_t Uint128Low64(uint128 v) { return v.lo_; }

constexpr uint64_t Uint128High64(uint128 v) { return v.hi_; }

// Constructors from integer types.

#if defined(ABSL_IS_LITTLE_ENDIAN)

constexpr uint128::uint128(uint64_t high, uint64_t low) : lo_{low}, hi_{high} {}

constexpr uint128::uint128(int v)
    : lo_{static_cast<uint64_t>(v)},
      hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}
constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
    : lo_{static_cast<uint64_t>(v)},
      hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}
constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
    : lo_{static_cast<uint64_t>(v)},
      hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}

constexpr uint128::uint128(unsigned int v) : lo_{v}, hi_{0} {}
// NOLINTNEXTLINE(runtime/int)
constexpr uint128::uint128(unsigned long v) : lo_{v}, hi_{0} {}
// NOLINTNEXTLINE(runtime/int)
constexpr uint128::uint128(unsigned long long v) : lo_{v}, hi_{0} {}

constexpr uint128::uint128(int128 v)
    : lo_{Int128Low64(v)}, hi_{static_cast<uint64_t>(Int128High64(v))} {}

#elif defined(ABSL_IS_BIG_ENDIAN)

constexpr uint128::uint128(uint64_t high, uint64_t low) : hi_{high}, lo_{low} {}

constexpr uint128::uint128(int v)
    : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
      lo_{static_cast<uint64_t>(v)} {}
constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
    : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
      lo_{static_cast<uint64_t>(v)} {}
constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
    : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
      lo_{static_cast<uint64_t>(v)} {}

constexpr uint128::uint128(unsigned int v) : hi_{0}, lo_{v} {}
// NOLINTNEXTLINE(runtime/int)
constexpr uint128::uint128(unsigned long v) : hi_{0}, lo_{v} {}
// NOLINTNEXTLINE(runtime/int)
constexpr uint128::uint128(unsigned long long v) : hi_{0}, lo_{v} {}

constexpr uint128::uint128(int128 v)
    : hi_{static_cast<uint64_t>(Int128High64(v))}, lo_{Int128Low64(v)} {}

#else  // byte order
#error "Unsupported byte order: must be little-endian or big-endian."
#endif  // byte order

// Conversion operators to integer types.

constexpr uint128::operator bool() const { return lo_ || hi_; }

constexpr uint128::operator char() const { return static_cast<char>(lo_); }

constexpr uint128::operator signed char() const {
  return static_cast<signed char>(lo_);
}

constexpr uint128::operator unsigned char() const {
  return static_cast<unsigned char>(lo_);
}

constexpr uint128::operator char16_t() const {
  return static_cast<char16_t>(lo_);
}

constexpr uint128::operator char32_t() const {
  return static_cast<char32_t>(lo_);
}

// NOLINTNEXTLINE(runtime/int)
constexpr uint128::operator short() const { return static_cast<short>(lo_); }

constexpr uint128::operator unsigned short() const {  // NOLINT(runtime/int)
  return static_cast<unsigned short>(lo_);            // NOLINT(runtime/int)
}

constexpr uint128::operator int() const { return static_cast<int>(lo_); }

constexpr uint128::operator unsigned int() const {
  return static_cast<unsigned int>(lo_);
}

// NOLINTNEXTLINE(runtime/int)
constexpr uint128::operator long() const { return static_cast<long>(lo_); }

constexpr uint128::operator unsigned long() const {  // NOLINT(runtime/int)
  return static_cast<unsigned long>(lo_);            // NOLINT(runtime/int)
}

constexpr uint128::operator long long() const {  // NOLINT(runtime/int)
  return static_cast<long long>(lo_);            // NOLINT(runtime/int)
}

constexpr uint128::operator unsigned long long() const {  // NOLINT(runtime/int)
  return static_cast<unsigned long long>(lo_);            // NOLINT(runtime/int)
}
// Conversion operators to floating point types.

inline uint128::operator float() const {
  return static_cast<float>(lo_) + std::ldexp(static_cast<float>(hi_), 64);
}

inline uint128::operator double() const {
  return static_cast<double>(lo_) + std::ldexp(static_cast<double>(hi_), 64);
}

inline uint128::operator long double() const {
  return static_cast<long double>(lo_) +
         std::ldexp(static_cast<long double>(hi_), 64);
}

// Comparison operators.

constexpr bool operator==(uint128 lhs, uint128 rhs) {
return (Uint128Low64(lhs) == Uint128Low64(rhs) &&
          Uint128High64(lhs) == Uint128High64(rhs));
}

constexpr bool operator!=(uint128 lhs, uint128 rhs) { return !(lhs == rhs); }

constexpr bool operator<(uint128 lhs, uint128 rhs) {
return (Uint128High64(lhs) == Uint128High64(rhs))
            ? (Uint128Low64(lhs) < Uint128Low64(rhs))
            : (Uint128High64(lhs) < Uint128High64(rhs));
}

constexpr bool operator>(uint128 lhs, uint128 rhs) { return rhs < lhs; }

constexpr bool operator<=(uint128 lhs, uint128 rhs) { return !(rhs < lhs); }

constexpr bool operator>=(uint128 lhs, uint128 rhs) { return !(lhs < rhs); }

// Unary operators.

constexpr inline uint128 operator+(uint128 val) { return val; }

constexpr inline int128 operator+(int128 val) { return val; }

constexpr uint128 operator-(uint128 val) {
return MakeUint128(
    ~Uint128High64(val) + static_cast<unsigned long>(Uint128Low64(val) == 0),
    ~Uint128Low64(val) + 1);
}

constexpr inline bool operator!(uint128 val) {
return !Uint128High64(val) && !Uint128Low64(val);
}

// Logical operators.

constexpr inline uint128 operator~(uint128 val) {
  return MakeUint128(~Uint128High64(val), ~Uint128Low64(val));
}

constexpr inline uint128 operator|(uint128 lhs, uint128 rhs) {
  return MakeUint128(Uint128High64(lhs) | Uint128High64(rhs),
                     Uint128Low64(lhs) | Uint128Low64(rhs));
}

constexpr inline uint128 operator&(uint128 lhs, uint128 rhs) {
  return MakeUint128(Uint128High64(lhs) & Uint128High64(rhs),
                     Uint128Low64(lhs) & Uint128Low64(rhs));
}

constexpr inline uint128 operator^(uint128 lhs, uint128 rhs) {
  return MakeUint128(Uint128High64(lhs) ^ Uint128High64(rhs),
                     Uint128Low64(lhs) ^ Uint128Low64(rhs));
}

inline uint128& uint128::operator|=(uint128 other) {
  *this = *this | other;
  return *this;
}

inline uint128& uint128::operator&=(uint128 other) {
  *this = *this & other;
  return *this;
}

inline uint128& uint128::operator^=(uint128 other) {
  *this = *this ^ other;
  return *this;
}

// Arithmetic operators.

constexpr uint128 operator<<(uint128 lhs, int amount) {
  // uint64_t shifts of >= 64 are undefined, so we will need some
  // special-casing.
  return amount >= 64  ? MakeUint128(Uint128Low64(lhs) << (amount - 64), 0)
         : amount == 0 ? lhs
                       : MakeUint128((Uint128High64(lhs) << amount) |
                                         (Uint128Low64(lhs) >> (64 - amount)),
                                     Uint128Low64(lhs) << amount);
}

constexpr uint128 operator>>(uint128 lhs, int amount) {
  // uint64_t shifts of >= 64 are undefined, so we will need some
  // special-casing.
  return amount >= 64  ? MakeUint128(0, Uint128High64(lhs) >> (amount - 64))
         : amount == 0 ? lhs
                       : MakeUint128(Uint128High64(lhs) >> amount,
                                     (Uint128Low64(lhs) >> amount) |
                                         (Uint128High64(lhs) << (64 - amount)));
}

namespace int128_internal {
constexpr uint128 AddResult(uint128 result, uint128 lhs) {
  // check for carry
  return (Uint128Low64(result) < Uint128Low64(lhs))
             ? MakeUint128(Uint128High64(result) + 1, Uint128Low64(result))
             : result;
}
}  // namespace int128_internal

constexpr uint128 operator+(uint128 lhs, uint128 rhs) {
  return int128_internal::AddResult(
      MakeUint128(Uint128High64(lhs) + Uint128High64(rhs),
                  Uint128Low64(lhs) + Uint128Low64(rhs)),
      lhs);
}

namespace int128_internal {
constexpr uint128 SubstructResult(uint128 result, uint128 lhs, uint128 rhs) {
  // check for carry
  return (Uint128Low64(lhs) < Uint128Low64(rhs))
             ? MakeUint128(Uint128High64(result) - 1, Uint128Low64(result))
             : result;
}
}  // namespace int128_internal

constexpr uint128 operator-(uint128 lhs, uint128 rhs) {
  return int128_internal::SubstructResult(
      MakeUint128(Uint128High64(lhs) - Uint128High64(rhs),
                  Uint128Low64(lhs) - Uint128Low64(rhs)),
      lhs, rhs);
}

inline uint128 operator*(uint128 lhs, uint128 rhs) {
  uint64_t a32 = Uint128Low64(lhs) >> 32;
  uint64_t a00 = Uint128Low64(lhs) & 0xffffffff;
  uint64_t b32 = Uint128Low64(rhs) >> 32;
  uint64_t b00 = Uint128Low64(rhs) & 0xffffffff;
  uint128 result =
      MakeUint128(Uint128High64(lhs) * Uint128Low64(rhs) +
                      Uint128Low64(lhs) * Uint128High64(rhs) + a32 * b32,
                  a00 * b00);
  result += uint128(a32 * b00) << 32;
  result += uint128(a00 * b32) << 32;
  return result;
}

// Increment/decrement operators.

inline uint128 uint128::operator++(int) {
  uint128 tmp(*this);
  *this += 1;
  return tmp;
}

inline uint128 uint128::operator--(int) {
  uint128 tmp(*this);
  *this -= 1;
  return tmp;
}

inline uint128& uint128::operator++() {
  *this += 1;
  return *this;
}

inline uint128& uint128::operator--() {
  *this -= 1;
  return *this;
}

constexpr int128 MakeInt128(int64_t high, uint64_t low) {
  return int128(high, low);
}

// Assignment from integer types.
inline int128& int128::operator=(int v) { return *this = int128(v); }

inline int128& int128::operator=(unsigned int v) { return *this = int128(v); }

inline int128& int128::operator=(long v) {  // NOLINT(runtime/int)
  return *this = int128(v);
}

// NOLINTNEXTLINE(runtime/int)
inline int128& int128::operator=(unsigned long v) { return *this = int128(v); }

// NOLINTNEXTLINE(runtime/int)
inline int128& int128::operator=(long long v) { return *this = int128(v); }

// NOLINTNEXTLINE(runtime/int)
inline int128& int128::operator=(unsigned long long v) {
  return *this = int128(v);
}

// Arithmetic operators.
constexpr int128 operator-(int128 v);
constexpr int128 operator+(int128 lhs, int128 rhs);
constexpr int128 operator-(int128 lhs, int128 rhs);
int128 operator*(int128 lhs, int128 rhs);
int128 operator/(int128 lhs, int128 rhs);
int128 operator%(int128 lhs, int128 rhs);
constexpr int128 operator|(int128 lhs, int128 rhs);
constexpr int128 operator&(int128 lhs, int128 rhs);
constexpr int128 operator^(int128 lhs, int128 rhs);
constexpr int128 operator<<(int128 lhs, int amount);
constexpr int128 operator>>(int128 lhs, int amount);

inline int128& int128::operator+=(int128 other) {
  *this = *this + other;
  return *this;
}

inline int128& int128::operator-=(int128 other) {
  *this = *this - other;
  return *this;
}

inline int128& int128::operator*=(int128 other) {
  *this = *this * other;
  return *this;
}

inline int128& int128::operator/=(int128 other) {
  *this = *this / other;
  return *this;
}

inline int128& int128::operator%=(int128 other) {
  *this = *this % other;
  return *this;
}

inline int128& int128::operator|=(int128 other) {
  *this = *this | other;
  return *this;
}

inline int128& int128::operator&=(int128 other) {
  *this = *this & other;
  return *this;
}

inline int128& int128::operator^=(int128 other) {
  *this = *this ^ other;
  return *this;
}

inline int128& int128::operator<<=(int amount) {
  *this = *this << amount;
  return *this;
}

inline int128& int128::operator>>=(int amount) {
  *this = *this >> amount;
  return *this;
}

// Forward declaration for comparison operators.
constexpr bool operator!=(int128 lhs, int128 rhs);

inline int
CountLeadingZeroes64(uint64_t x) {
int zeroes = 60;
if (x >> 32) {
zeroes -= 32;
x >>= 32;
}
if (x >> 16) {
zeroes -= 16;
x >>= 16;
}
if (x >> 8) {
zeroes -= 8;
x >>= 8;
}
if (x >> 4) {
zeroes -= 4;
x >>= 4;
}
return "\4\3\2\2\1\1\1\1\0\0\0\0\0\0\0"[x] + zeroes;
}

inline int MSB(uint128 n) {
  if (uint64_t hi = Uint128High64(n)) {
    return 127 - CountLeadingZeroes64(hi);
  }
  const uint64_t low = Uint128Low64(n);
  return 63 - CountLeadingZeroes64(low);
}

// Long division/modulo for uint128 implemented using the shift-subtract
// division algorithm adapted from:
// https://stackoverflow.com/questions/5386377/division-without-using
inline void DivModImpl(uint128 dividend, uint128 divisor, uint128* quotient_ret,
                       uint128* remainder_ret) {
  assert(divisor != 0);

  if (divisor > dividend) {
    *quotient_ret = 0;
    *remainder_ret = dividend;
    return;
  }

  if (divisor == dividend) {
    *quotient_ret = 1;
    *remainder_ret = 0;
    return;
  }

  uint128 denominator = divisor;
  uint128 quotient = 0;

  // Left aligns the MSB of the denominator and the dividend.
  const int shift = MSB(dividend) - MSB(denominator);
  denominator <<= shift;

  // Uses shift-subtract algorithm to divide dividend by denominator. The
  // remainder will be left in dividend.
  for (int i = 0; i <= shift; ++i) {
    quotient <<= 1;
    if (dividend >= denominator) {
      dividend -= denominator;
      quotient |= 1;
    }
    denominator >>= 1;
  }

  *quotient_ret = quotient;
  *remainder_ret = dividend;
}

template <typename T>
uint128 MakeUint128FromFloat(T v) {
  static_assert(std::is_floating_point<T>::value, "");

  // Rounding behavior is towards zero, same as for built-in types.

  // Undefined behavior if v is NaN or cannot fit into uint128.
  assert(std::isfinite(v) && v > -1 &&
         (std::numeric_limits<T>::max_exponent <= 128 ||
          v < std::ldexp(static_cast<T>(1), 128)));

  if (v >= std::ldexp(static_cast<T>(1), 64)) {
    uint64_t hi = static_cast<uint64_t>(std::ldexp(v, -64));
    uint64_t lo = static_cast<uint64_t>(v - std::ldexp(static_cast<T>(hi), 64));
    return MakeUint128(hi, lo);
  }

  return MakeUint128(0, static_cast<uint64_t>(v));
}

uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}

uint128 operator/(uint128 lhs, uint128 rhs) {
  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(lhs, rhs, &quotient, &remainder);
  return quotient;
}

uint128 operator%(uint128 lhs, uint128 rhs) {
  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(lhs, rhs, &quotient, &remainder);
  return remainder;
}

std::string Uint128ToFormattedString(uint128 v, std::ios_base::fmtflags flags) {
  // Select a divisor which is the largest power of the base < 2^64.
  uint128 div;
  int div_base_log;
  switch (flags & std::ios::basefield) {
    case std::ios::hex:
      div = 0x1000000000000000;  // 16^15
      div_base_log = 15;
      break;
    case std::ios::oct:
      div = 01000000000000000000000;  // 8^21
      div_base_log = 21;
      break;
    default:  // std::ios::dec
      div = 10000000000000000000u;  // 10^19
      div_base_log = 19;
      break;
  }

  // Now piece together the uint128 representation from three chunks of the
  // original value, each less than "div" and therefore representable as a
  // uint64_t.
  std::ostringstream os;
  std::ios_base::fmtflags copy_mask =
      std::ios::basefield | std::ios::showbase | std::ios::uppercase;
  os.setf(flags & copy_mask, copy_mask);
  uint128 high = v;
  uint128 low;
  DivModImpl(high, div, &high, &low);
  uint128 mid;
  DivModImpl(high, div, &high, &mid);
  if (Uint128Low64(high) != 0) {
    os << Uint128Low64(high);
    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
    os << Uint128Low64(mid);
    os << std::setw(div_base_log);
  } else if (Uint128Low64(mid) != 0) {
    os << Uint128Low64(mid);
    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
  }
  os << Uint128Low64(low);
  return os.str();
}

std::string uint128::ToString() const {
  return Uint128ToFormattedString(*this, std::ios_base::dec);
}

std::ostream& operator<<(std::ostream& os, uint128 v) {
  std::ios_base::fmtflags flags = os.flags();
  std::string rep = Uint128ToFormattedString(v, flags);

  // Add the requisite padding.
  std::streamsize width = os.width(0);
  if (static_cast<size_t>(width) > rep.size()) {
    const size_t count = static_cast<size_t>(width) - rep.size();
    std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
    if (adjustfield == std::ios::left) {
      rep.append(count, os.fill());
    } else if (adjustfield == std::ios::internal &&
               (flags & std::ios::showbase) &&
               (flags & std::ios::basefield) == std::ios::hex && v != 0) {
      rep.insert(size_t{2}, count, os.fill());
    } else {
      rep.insert(size_t{0}, count, os.fill());
    }
  }

  return os << rep;
}

uint128 UnsignedAbsoluteValue(int128 v) {
  // Cast to uint128 before possibly negating because -Int128Min() is undefined.
  return Int128High64(v) < 0 ? -uint128(v) : uint128(v);
}

template <typename T>
int128 MakeInt128FromFloat(T v) {
  // Conversion when v is NaN or cannot fit into int128 would be undefined
  // behavior if using an intrinsic 128-bit integer.
  assert(std::isfinite(v) && (std::numeric_limits<T>::max_exponent <= 127 ||
                              (v >= -std::ldexp(static_cast<T>(1), 127) &&
                               v < std::ldexp(static_cast<T>(1), 127))));

  // We must convert the absolute value and then negate as needed, because
  // floating point types are typically sign-magnitude. Otherwise, the
  // difference between the high and low 64 bits when interpreted as two's
  // complement overwhelms the precision of the mantissa.
  uint128 result = v < 0 ? -MakeUint128FromFloat(-v) : MakeUint128FromFloat(v);
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
                    Uint128Low64(result));
}

int128::int128(float v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(double v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(long double v) : int128(MakeInt128FromFloat(v)) {}

constexpr uint64_t Int128Low64(int128 v) { return v.lo_; }

constexpr int64_t Int128High64(int128 v) { return v.hi_; }

#if defined(ABSL_IS_LITTLE_ENDIAN)

constexpr int128::int128(int64_t high, uint64_t low) : lo_(low), hi_(high) {}

constexpr int128::int128(int v)
    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}
constexpr int128::int128(long v)  // NOLINT(runtime/int)
    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}
constexpr int128::int128(long long v)  // NOLINT(runtime/int)
    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}

constexpr int128::int128(unsigned int v) : lo_{v}, hi_{0} {}
// NOLINTNEXTLINE(runtime/int)
constexpr int128::int128(unsigned long v) : lo_{v}, hi_{0} {}
// NOLINTNEXTLINE(runtime/int)
constexpr int128::int128(unsigned long long v) : lo_{v}, hi_{0} {}

constexpr int128::int128(uint128 v)
    : lo_{Uint128Low64(v)}, hi_{static_cast<int64_t>(Uint128High64(v))} {}

#elif defined(ABSL_IS_BIG_ENDIAN)

constexpr int128::int128(int64_t high, uint64_t low) : hi_{high}, lo_{low} {}

constexpr int128::int128(int v)
    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}
constexpr int128::int128(long v)  // NOLINT(runtime/int)
    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}
constexpr int128::int128(long long v)  // NOLINT(runtime/int)
    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}

constexpr int128::int128(unsigned int v) : hi_{0}, lo_{v} {}
// NOLINTNEXTLINE(runtime/int)
constexpr int128::int128(unsigned long v) : hi_{0}, lo_{v} {}
// NOLINTNEXTLINE(runtime/int)
constexpr int128::int128(unsigned long long v) : hi_{0}, lo_{v} {}

constexpr int128::int128(uint128 v)
    : hi_{static_cast<int64_t>(Uint128High64(v))}, lo_{Uint128Low64(v)} {}

#else  // byte order
#error "Unsupported byte order: must be little-endian or big-endian."
#endif  // byte order

constexpr int128::operator bool() const { return lo_ || hi_; }

constexpr int128::operator char() const {
  // NOLINTNEXTLINE(runtime/int)
  return static_cast<char>(static_cast<long long>(*this));
}

constexpr int128::operator signed char() const {
  // NOLINTNEXTLINE(runtime/int)
  return static_cast<signed char>(static_cast<long long>(*this));
}

constexpr int128::operator unsigned char() const {
  return static_cast<unsigned char>(lo_);
}

constexpr int128::operator char16_t() const {
  return static_cast<char16_t>(lo_);
}

constexpr int128::operator char32_t() const {
  return static_cast<char32_t>(lo_);
}

constexpr int128::operator short() const {  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  return static_cast<short>(static_cast<long long>(*this));
}

constexpr int128::operator unsigned short() const {  // NOLINT(runtime/int)
  return static_cast<unsigned short>(lo_);           // NOLINT(runtime/int)
}

constexpr int128::operator int() const {
  // NOLINTNEXTLINE(runtime/int)
  return static_cast<int>(static_cast<long long>(*this));
}

constexpr int128::operator unsigned int() const {
  return static_cast<unsigned int>(lo_);
}

constexpr int128::operator long() const {  // NOLINT(runtime/int)
  // NOLINTNEXTLINE(runtime/int)
  return static_cast<long>(static_cast<long long>(*this));
}

constexpr int128::operator unsigned long() const {  // NOLINT(runtime/int)
  return static_cast<unsigned long>(lo_);           // NOLINT(runtime/int)
}

constexpr int128::operator long long() const {  // NOLINT(runtime/int)
  // We don't bother checking the value of hi_. If *this < 0, lo_'s high bit
  // must be set in order for the value to fit into a long long. Conversely, if
  // lo_'s high bit is set, *this must be < 0 for the value to fit.
  return int128_internal::BitCastToSigned(lo_);
}

constexpr int128::operator unsigned long long() const {  // NOLINT(runtime/int)
  return static_cast<unsigned long long>(lo_);           // NOLINT(runtime/int)
}

inline int128::operator float() const {
  // We must convert the absolute value and then negate as needed, because
  // floating point types are typically sign-magnitude. Otherwise, the
  // difference between the high and low 64 bits when interpreted as two's
  // complement overwhelms the precision of the mantissa.
  //
  // Also check to make sure we don't negate Int128Min()
  return hi_ < 0 && *this != Int128Min()
             ? -static_cast<float>(-*this)
             : static_cast<float>(lo_) +
                   std::ldexp(static_cast<float>(hi_), 64);
}

inline int128::operator double() const {
  // See comment in int128::operator float() above.
  return hi_ < 0 && *this != Int128Min()
             ? -static_cast<double>(-*this)
             : static_cast<double>(lo_) +
                   std::ldexp(static_cast<double>(hi_), 64);
}

inline int128::operator long double() const {
  // See comment in int128::operator float() above.
  return hi_ < 0 && *this != Int128Min()
             ? -static_cast<long double>(-*this)
             : static_cast<long double>(lo_) +
                   std::ldexp(static_cast<long double>(hi_), 64);
}

// Comparison operators.

constexpr bool operator==(int128 lhs, int128 rhs) {
  return (Int128Low64(lhs) == Int128Low64(rhs) &&
          Int128High64(lhs) == Int128High64(rhs));
}

constexpr bool operator!=(int128 lhs, int128 rhs) { return !(lhs == rhs); }

constexpr bool operator<(int128 lhs, int128 rhs) {
  return (Int128High64(lhs) == Int128High64(rhs))
             ? (Int128Low64(lhs) < Int128Low64(rhs))
             : (Int128High64(lhs) < Int128High64(rhs));
}

constexpr bool operator>(int128 lhs, int128 rhs) {
  return (Int128High64(lhs) == Int128High64(rhs))
             ? (Int128Low64(lhs) > Int128Low64(rhs))
             : (Int128High64(lhs) > Int128High64(rhs));
}

constexpr bool operator<=(int128 lhs, int128 rhs) { return !(lhs > rhs); }

constexpr bool operator>=(int128 lhs, int128 rhs) { return !(lhs < rhs); }

// Unary operators.

constexpr int128 operator-(int128 v) {
  return MakeInt128(~Int128High64(v) + (Int128Low64(v) == 0),
                    ~Int128Low64(v) + 1);
}

constexpr bool operator!(int128 v) {
  return !Int128Low64(v) && !Int128High64(v);
}

constexpr int128 operator~(int128 val) {
  return MakeInt128(~Int128High64(val), ~Int128Low64(val));
}

//Organized by me (from int128_no_intrinsic.inc)

//Organized by me -end
int128 operator/(int128 lhs, int128 rhs) {
  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.

  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
             &quotient, &remainder);
  if ((Int128High64(lhs) < 0) != (Int128High64(rhs) < 0)) quotient = -quotient;
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(quotient)),
                    Uint128Low64(quotient));
}

int128 operator%(int128 lhs, int128 rhs) {
  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.

  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
             &quotient, &remainder);
  if (Int128High64(lhs) < 0) remainder = -remainder;
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(remainder)),
                    Uint128Low64(remainder));
}

std::string int128::ToString() const {
  std::string rep;
  if (Int128High64(*this) < 0) rep = "-";
  rep.append(Uint128ToFormattedString(UnsignedAbsoluteValue(*this),
                                      std::ios_base::dec));
  return rep;
}

std::ostream& operator<<(std::ostream& os, int128 v) {
  std::ios_base::fmtflags flags = os.flags();
  std::string rep;

  // Add the sign if needed.
  bool print_as_decimal =
      (flags & std::ios::basefield) == std::ios::dec ||
      (flags & std::ios::basefield) == std::ios_base::fmtflags();
  if (print_as_decimal) {
    if (Int128High64(v) < 0) {
      rep = "-";
    } else if (flags & std::ios::showpos) {
      rep = "+";
    }
  }

  rep.append(Uint128ToFormattedString(
      print_as_decimal ? UnsignedAbsoluteValue(v) : uint128(v), os.flags()));

  // Add the requisite padding.
  std::streamsize width = os.width(0);
  if (static_cast<size_t>(width) > rep.size()) {
    const size_t count = static_cast<size_t>(width) - rep.size();
    switch (flags & std::ios::adjustfield) {
      case std::ios::left:
        rep.append(count, os.fill());
        break;
      case std::ios::internal:
        if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) {
          rep.insert(size_t{1}, count, os.fill());
        } else if ((flags & std::ios::basefield) == std::ios::hex &&
                   (flags & std::ios::showbase) && v != 0) {
          rep.insert(size_t{2}, count, os.fill());
        } else {
          rep.insert(size_t{0}, count, os.fill());
        }
        break;
      default:  // std::ios::right
        rep.insert(size_t{0}, count, os.fill());
        break;
    }
  }

  return os << rep;
}

namespace int128_internal {
constexpr int128 SignedAddResult(int128 result, int128 lhs) {
  // check for carry
  return (Int128Low64(result) < Int128Low64(lhs))
             ? MakeInt128(Int128High64(result) + 1, Int128Low64(result))
             : result;
}
}  // namespace int128_internal
constexpr int128 operator+(int128 lhs, int128 rhs) {
  return int128_internal::SignedAddResult(
      MakeInt128(Int128High64(lhs) + Int128High64(rhs),
                 Int128Low64(lhs) + Int128Low64(rhs)),
      lhs);
}

namespace int128_internal {
constexpr int128 SignedSubstructResult(int128 result, int128 lhs, int128 rhs) {
  // check for carry
  return (Int128Low64(lhs) < Int128Low64(rhs))
             ? MakeInt128(Int128High64(result) - 1, Int128Low64(result))
             : result;
}
}  // namespace int128_internal
constexpr int128 operator-(int128 lhs, int128 rhs) {
  return int128_internal::SignedSubstructResult(
      MakeInt128(Int128High64(lhs) - Int128High64(rhs),
                 Int128Low64(lhs) - Int128Low64(rhs)),
      lhs, rhs);
}

inline int128 operator*(int128 lhs, int128 rhs) {
  return MakeInt128(
      int128_internal::BitCastToSigned(Uint128High64(uint128(lhs) * rhs)),
      Uint128Low64(uint128(lhs) * rhs));
}

inline int128 int128::operator++(int) {
  int128 tmp(*this);
  *this += 1;
  return tmp;
}

inline int128 int128::operator--(int) {
  int128 tmp(*this);
  *this -= 1;
  return tmp;
}

inline int128& int128::operator++() {
  *this += 1;
  return *this;
}

inline int128& int128::operator--() {
  *this -= 1;
  return *this;
}

constexpr int128 operator|(int128 lhs, int128 rhs) {
  return MakeInt128(Int128High64(lhs) | Int128High64(rhs),
                    Int128Low64(lhs) | Int128Low64(rhs));
}

constexpr int128 operator&(int128 lhs, int128 rhs) {
  return MakeInt128(Int128High64(lhs) & Int128High64(rhs),
                    Int128Low64(lhs) & Int128Low64(rhs));
}

constexpr int128 operator^(int128 lhs, int128 rhs) {
  return MakeInt128(Int128High64(lhs) ^ Int128High64(rhs),
                    Int128Low64(lhs) ^ Int128Low64(rhs));
}

constexpr int128 operator<<(int128 lhs, int amount) {
  // int64_t shifts of >= 63 are undefined, so we need some special-casing.
  assert(amount >= 0 && amount < 127);
  if (amount <= 0) {
    return lhs;
  } else if (amount < 63) {
    return MakeInt128(
        (Int128High64(lhs) << amount) |
            static_cast<int64_t>(Int128Low64(lhs) >> (64 - amount)),
        Int128Low64(lhs) << amount);
  } else if (amount == 63) {
    return MakeInt128(((Int128High64(lhs) << 32) << 31) |
                          static_cast<int64_t>(Int128Low64(lhs) >> 1),
                      (Int128Low64(lhs) << 32) << 31);
  } else if (amount == 127) {
    return MakeInt128(static_cast<int64_t>(Int128Low64(lhs) << 63), 0);
  } else if (amount > 127) {
    return MakeInt128(0, 0);
  } else {
    // amount >= 64 && amount < 127
    return MakeInt128(static_cast<int64_t>(Int128Low64(lhs) << (amount - 64)),
                      0);
  }
}

constexpr int128 operator>>(int128 lhs, int amount) {
  // int64_t shifts of >= 63 are undefined, so we need some special-casing.
  assert(amount >= 0 && amount < 127);
  if (amount <= 0) {
    return lhs;
  } else if (amount < 63) {
    return MakeInt128(
        Int128High64(lhs) >> amount,
        Int128Low64(lhs) >> amount | static_cast<uint64_t>(Int128High64(lhs))
                                         << (64 - amount));
  } else if (amount == 63) {
    return MakeInt128((Int128High64(lhs) >> 32) >> 31,
                      static_cast<uint64_t>(Int128High64(lhs) << 1) |
                          (Int128Low64(lhs) >> 32) >> 31);

  } else if (amount >= 127) {
    return MakeInt128((Int128High64(lhs) >> 32) >> 31,
                      static_cast<uint64_t>((Int128High64(lhs) >> 32) >> 31));
  } else {
    // amount >= 64 && amount < 127
    return MakeInt128(
        (Int128High64(lhs) >> 32) >> 31,
        static_cast<uint64_t>(Int128High64(lhs) >> (amount - 64)));
  }
}

//cpp ends

}  // namespace absl

int main(void){
    absl::int128 x = (long long)2e18;
    x *= 10;
    std::cout << x << " " << absl::MSB(x) << "\n";
    absl::uint128 y = (x/10) * (x/10);
    cout << y << "\n";
    while(true){
        int a = 0;
        printf("Input a");
        cin >> a;
        if(!a) break;
        absl::int128 z = (absl::int128(a) << 126);
        absl::uint128 w = z;
        cout << z << " " << w << "\n";
    }
}