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<처음 아이디어 => 사유: 시간 초과>

import java.util.*;

class Main {  
  public static void main(String args[]) { 
    Scanner sc = new Scanner(System.in);
    StringBuilder sb = new StringBuilder();
    int T = sc.nextInt();

    for(int i = 0; i < T; i++){
      int year = 0;
      int M = sc.nextInt();
      int N = sc.nextInt();
      int x = sc.nextInt();
      int y = sc.nextInt();
      
      while(true){
        year++;
        if((year - M) % M == x && (year - N) % N == y ){
          break;
        }

        if((year - M) % M == 0 && (year - N) % N == 0 ){
          year = -1;
          break;
        }
      }
      sb.append(year).append('\n');
    }
    System.out.println(sb);
  } 
}

<변경된 아이디어>

import java.util.Scanner;

    public class Main {

        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            StringBuilder sb = new StringBuilder();
            int T = sc.nextInt();


            for (int s = 0; s < T; s++) {

                boolean check = false;
                int m = sc.nextInt();
                int n = sc.nextInt();
                int x = sc.nextInt() - 1;
                int y = sc.nextInt() - 1;

                for (int i = x; i < (n * m); i += m) {
                    if (i % n == y) {
                        sb.append(i + 1).append('\n');
                        check = true;
                        break;
                    }
                }

                if (!check) {
                    sb.append(-1).append('\n');
                }
            }
            System.out.println(sb);
        }
    }