6064.cpp

// Authored by : BaaaaaaaaaaarkingDog
// Co-authored by : -
// http://boj.kr/a4aee25a9bbf4f739b3da815b625b3fd
#include <bits/stdc++.h>
using namespace std;

int gcd(int a, int b){
  if(a == 0) return b;
  return gcd(b%a, a);
}

int lcm(int a, int b){
  return a / gcd(a, b) * b;
}

int solve(int m, int n, int x, int y){
  if(x == m) x = 0;
  if(y == n) y = 0;
  int l = lcm(m, n);
  for(int i = x; i <= l; i += m){
    if(i == 0) continue;
    if(i % n == y)
      return i;
  }
  return -1;
}

int main(void){
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  while(n--){
    int m,n,x,y;
    cin >> m >> n >> x >> y;
    cout << solve(m, n, x, y) << '\n';
  }
}