二次剩余模板

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


typedef long long ll;
int t;
ll n, p;
ll w;



struct num {  //建立一个复数域



  ll x, y;
};



num mul(num a, num b, ll p) {  //复数乘法
  num ans = {0, 0};
  ans.x = ((a.x * b.x % p + a.y * b.y % p * w % p) % p + p) % p;
  ans.y = ((a.x * b.y % p + a.y * b.x % p) % p + p) % p;
  return ans;
}



ll binpow_real(ll a, ll b, ll p) {  //实部快速幂
  ll ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % p;
    a = a * a % p;
    b >>= 1;
  }
  return ans % p;
}



ll binpow_imag(num a, ll b, ll p) {  //虚部快速幂
  num ans = {1, 0};
  while (b) {
    if (b & 1) ans = mul(ans, a, p);
    a = mul(a, a, p);
    b >>= 1;
  }
  return ans.x % p;
}



ll cipolla(ll n, ll p) {
  n %= p;
  if (p == 2) return n;
  if (binpow_real(n, (p - 1) / 2, p) == p - 1) return -1;
  ll a;
  while (1) {  //生成随机数再检验找到满足非二次剩余的a
    a = rand() % p;
    w = ((a * a % p - n) % p + p) % p;
    if (binpow_real(w, (p - 1) / 2, p) == p - 1) break;
  }
  num x = {a, 1};
  return binpow_imag(x, (p + 1) / 2, p);
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld%lld",&n,&p);
        if(!n)
        {
            puts("0");
            continue;
        }
        else
        {   
            ll x1=cipolla(n,p),x2;
            if(x1==-1) 
            {
                puts("Hola!");
            }
            else
            {   
                x2=p-x1;
                if(x1==x2) printf("%lld
",x1);
                else
                {
                    if(x1>x2) swap(x1,x2);
                    printf("%lld %lld
",x1,x2);
                }
                
            }



        }
    }
    return 0;
}