namespace number_theory { ll gcd(ll x, ll y) { if (x == 0) return y; if (y == 0) return x; return gcd(y, x % y); } bool isprime(ll n) { if (n <= 1) return false; if (n <= 3) return true;

  if (n % 2 == 0 || n % 3 == 0) return false; 

  for (ll i = 5; i * i <= n; i += 6) 
    if (n % i == 0 || n % (i+2) == 0) 
      return false; 

  return true; 
} 

bool prime[15000105]; 
void sieve(int n) { 
  for (ll i = 0; i <= n; i++) prime[i] = 1;
  for (ll p = 2; p * p <= n; p++) { 
    if (prime[p] == true) { 
      for (ll i = p * p; i <= n; i += p) 
       prime[i] = false; 
    } 
  } 
  prime[1] = prime[0] = 0;
} 

vector<ll> primelist;
bool __primes_generated__ = 0;

void genprimes(int n) {
  __primes_generated__ = 1;
  sieve(n + 1);
  for (ll i = 2; i <= n; i++) if (prime[i]) primelist.push_back(i);
}

vector<ll> factors(ll n) {
  if (!__primes_generated__) {
    cerr << "Call genprimes you dope" << endl;
    exit(1);
  }
  vector<ll> facs;

  for (ll i = 0; primelist[i] * primelist[i] <= n && i < primelist.size(); i++) {
    if (n % primelist[i] == 0) {
      while (n % primelist[i] == 0) {
       n /= primelist[i];
       facs.push_back(primelist[i]);
      }
    }
  }
  if (n > 1) {
    facs.push_back(n);
  }
  sort(facs.begin(), facs.end());
  return facs;
}

vector<ll> getdivs(ll n) {
vector<ll> divs;
for (ll i = 1; i * i <= n; i++) {
  if (n % i == 0) {
    divs.push_back(i);
    divs.push_back(n / i);
  }
}

getunique(divs);
return divs;

} }

int maxx = 1e5; vector prime; prime.resize(maxx); for(int i =1;i<maxx;i++){ prime[i]=1; } for(int i =2;i<maxx;i++){ if(prime[i]==1){ for(int j =i;j<maxx;j+=i){ prime[j]=0; } } }

use long long double, SetPrecision(12)-sets the resolution of the variable ,fixed- cancels scientific notation.