#include<climits>

namespace RedshiftShine{
    
    using ll=unsigned long long;
    const ll ulmx=ULLONG_MAX;
    const ll shift=32;

    ll min(ll x,ll y){
        return x<y?x:y;
    }

    ll max(ll x,ll y){
        return x>y?x:y;
    }

    bool detect_overflow_add(ll x,ll y){
        return x+y<min(x,y);
    }

    bool detect_overflow_minus(ll x,ll y){
        return x-y>max(x,y);
    }

    class Custom_Unsigned_int128{
        private:
        ll higherInt,lowerInt;
        public:
        Custom_Unsigned_int128(){}

        template<typename _Tp>
        Custom_Unsigned_int128(_Tp x):
        higherInt(0),
        lowerInt(x){}

        template<typename _Tp>
        Custom_Unsigned_int128(_Tp x,_Tp y):
        higherInt(x),
        lowerInt(y){}
        
        Custom_Unsigned_int128
        (const Custom_Unsigned_int128& ele):
        higherInt(ele.higherInt),
        lowerInt(ele.lowerInt){}
        
        template<typename _Tp>
        Custom_Unsigned_int128
        operator=(const _Tp& x){
            higherInt=0;
            lowerInt=x;
        }

        Custom_Unsigned_int128
        operator=(const Custom_Unsigned_int128& x){
            higherInt=x.higherInt;
            lowerInt=x.lowerInt;
        }

        template<typename _Tp>
        Custom_Unsigned_int128
        operator+(const _Tp& x){
            return Custom_Unsigned_int128
            {
                higherInt+
                detect_overflow_add(lowerInt,x),
                lowerInt+x
            };
        }

        Custom_Unsigned_int128
        operator+(const Custom_Unsigned_int128& x){
            return Custom_Unsigned_int128
            {
                higherInt+x.higherInt+
                detect_overflow_add(lowerInt,x.lowerInt),
                lowerInt+x.lowerInt
            };
        }

        template<typename _Tp>
        Custom_Unsigned_int128
        operator-(const _Tp& x){
            return Custom_Unsigned_int128
            {
                higherInt-
                detect_overflow_minus(lowerInt,x),
                lowerInt-x
            };
        }

        Custom_Unsigned_int128
        operator-(const Custom_Unsigned_int128& x){
            return Custom_Unsigned_int128
            {
                higherInt-x.higherInt-
                detect_overflow_minus(lowerInt,x.lowerInt),
                lowerInt-x.lowerInt
            };
        }

        template<typename _Tp>
        Custom_Unsigned_int128
        operator&(const _Tp& x){
            return Custom_Unsigned_int128
            {
                higherInt,
                lowerInt&x
            };
        }

        Custom_Unsigned_int128
        operator&(const Custom_Unsigned_int128& x){
            return Custom_Unsigned_int128
            {
                higherInt&x.higherInt,
                lowerInt&x.lowerInt
            };
        }

        template<typename _Tp>
        Custom_Unsigned_int128
        operator|(const _Tp& x){
            return Custom_Unsigned_int128
            {
                higherInt,
                lowerInt|x
            };
        }

        Custom_Unsigned_int128
        operator|(const Custom_Unsigned_int128& x){
            return Custom_Unsigned_int128
            {
                higherInt|x.higherInt,
                lowerInt|x.lowerInt
            };
        }

        template<typename _Tp>
        Custom_Unsigned_int128
        operator^(const _Tp& x){
            return Custom_Unsigned_int128
            {
                higherInt,
                lowerInt^x
            };
        }

        Custom_Unsigned_int128
        operator^(const Custom_Unsigned_int128& x){
            return Custom_Unsigned_int128
            {
                higherInt^x.higherInt,
                lowerInt^x.lowerInt
            };
        }

    };

}