hdu 1576 扩展欧几里得

(A/B)%9973=K

A/B=K+9973*X

A=BK+9973*X*B

A%9973=n;

BK%9973=n;

BK=n+9973*Y

(K/n)*B+(-Y/n)*9973=GCD(B,9973)=1;

求出k/n，求出k

/*
    扩展欧几里得
    扩展欧几里德算法是用来在已知a, b求解一组x，y使得ax+by = Gcd(a, b) =d(解一定存在，根据数论中的相关定理)
*/
#include<cstdio>
#include<iostream>
#define ll long long

using namespace std;

ll x,y;
void gcd(ll a,ll b)
{
    if(b==0)
    {
        x = 1;
        y = 0;
        return ;
    }
    gcd(b,a%b);
    ll t = x;
    x = y;
    y = t-(a/b)*y;
}
int main()
{
    int t;
    int n,b;
    cin>>t;
    while(t--)
    {
        cin>>n>>b;
        gcd(b,9973);
        //x*=n;
        x = (x%9973+9973)%9973; //最小正数
        cout<<(x*n)%9973<<endl;
    }
    return 0;
}