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: Accepted)

import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int M = scanner.nextInt();
    char[] s = scanner.next().toCharArray();
    char[] t = scanner.next().toCharArray();

    System.out.println(solve(N, M, s, t));
  }

  private static long solve(int N, int M, char[] s, char[] t) {
    if (N > M) return solve(M, N, t, s);
    long gcd = gcd(N, M);
    long lsm = (long) N / gcd * M;
    for (int i = 0, j = 0; i < N && j < M; ) {
      if (s[i] != t[j]) return -1;
      i += N / gcd;
      j += M / gcd;
    }
    return lsm;
  }

  private static long gcd(long i, long j) {
    if (i > j) return gcd(j, i);
    while (i > 0) {
      long r = j % i;
      j = i;
      i = r;
    }
    return j;
  }
}