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.*;
public class Main{   
    public static void main(String[] args){
      Scanner sc = new Scanner(System.in);
      long n = sc.nextLong();
      long m = sc.nextLong();
      char[] s = sc.next().toCharArray();
      char[] t = sc.next().toCharArray();
      long l = lcm(n,m);
      Map<Long,Character> map = new HashMap<>();
      for(long i=0;i<n;i++)map.put((l/n)*i+1,s[(int)i]);
      for(long i=0;i<m;i++){
        if(map.containsKey((l/m)*i+1)&&t[(int)i]!=map.get((l/m)*i+1)){
          System.out.println(-1);
          return;
        }
      }
      System.out.println(l);
    }
    public static long lcm(long x, long y){
      return x*y/gcd(x,y);
    }
    public static long gcd(long x, long y){
      if(x < y)return gcd(y,x);
      if(y==0)return x;
      return gcd(y,x%y);
    }
}
class Pair{
    int a,b;

    Pair(int a, int b){
      this.a = a;
      this.b = b;
    }
}