参考资料： 扩展欧几里得算法
讲的很清晰简单，直接附代码

#include<iostream>
using namespace std;
int x2, y2; // 记录上一层的x，y
void exgcd(int a, int b, int& x, int& y){
    if(b == 0){
        x2 = 1;
        y2 = 0;
        return ;
    }

    exgcd(b, a % b, x, y);
    x = y2;  //递归回来时，用上层的x，y更新本层的x，y
    y = x2 - (a / b) * y2;
    x2 = x, y2 = y;
}

int main(){
    int n;
    cin >> n;
    while(n--){
        int a, b, x, y;
        cin >> a >> b;
        exgcd(a, b, x, y);
        cout << x << " " << y << endl;
    }
    return 0;
}