Problem:
Score : 300 points

Problem Statement

You are given a string S of length N and another string T of length M.
These strings consist of lowercase English letters.

A string X is called a good string when the following conditions are all met:

Let L be the length of X. L is divisible by both N and M.

Concatenating the 1-st, (\frac{L}{N}+1)-th, (2 \times \frac{L}{N}+1)-th, ..., ((N-1)\times\frac{L}{N}+1)-th characters of X, without changing the order, results in S.

Concatenating the 1-st, (\frac{L}{M}+1)-th, (2 \times \frac{L}{M}+1)-th, ..., ((M-1)\times\frac{L}{M}+1)-th characters of X, without changing the order, results in T.

Determine if there exists a good string. If it exists, find the length of the shortest such string.

Constraints

1 \leq N,M \leq 10^5

S and T consist of lowercase English letters.

|S|=N

|T|=M

Input

Input is given from Standard Input in the following format:

N M
S
T

Output

If a good string does not exist, print -1; if it exists, print the length of the shortest such string.

Sample Input 1

3 2
acp
ae

Sample Output 1

6

For example, the string accept is a good string.
There is no good string shorter than this, so the answer is 6.

Sample Input 2

6 3
abcdef
abc

Sample Output 2

-1

Sample Input 3

15 9
dnsusrayukuaiia
dujrunuma

Sample Output 3

45

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int M = sc.nextInt();
    String S = sc.next();
    String T = sc.next();
    if (S.charAt(0) != T.charAt(0)) {
      System.out.println(-1);
      return;
    }
    int gcd = calcGcd(N, M);
    if (gcd == -1) {
      System.out.println((long)N*M);
      return;
    }
    if (gcd == N || gcd == M) {
      int cycle = gcd == N ? N : M;
      String target = N >= M ? S : T;
      String key = N >= M ? T : S;
      if (key.charAt(0) != key.charAt(key.length()-1)) {
        System.out.println(-1);
        return;
      }
      for (int i = 0; i < target.length(); i+=cycle) {
        if (target.charAt(i) != key.charAt(i/cycle)) {
          System.out.println(-1);
          return;
        }
      }
      System.out.println(target.length());
      return;
    }
    System.out.println(gcd*(N/gcd)*(M/gcd));
  }
  
  private static int calcGcd(int n, int m) {
    for (int i = 2; i <= n && i <= m; i++) {
      if (n%i == 0 && m%i == 0) {
        return i;
      }
    }
    return -1;
  }
}