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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <set>
#include <numeric>
#include <algorithm>
#include <cstdlib>
#include <vector>

using namespace std;
int main() {
    int n, m, answer = -1, flag = 0;
    string s, t;
    cin >> n >> m;
    cin >> s >> t;
    int l = ((m / __gcd(m, n)) * n);

    if(s[0] == t[0]){
        int nx = (l / n);
        int mx = (l / m);
        
        answer = l;
        
        for(int i = 1; i < n; i++){
            for(int j = 1; j < m; j++){
                if(i * nx + 1 == j * mx + 1){
                    if(s[i] != t[j]){
                        flag = 1;
                        answer = -1;
                        break;
                    }
                }
                
            }
            if(flag == 1) break;
        }
    }

    cout << answer << endl;
    
}