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>

using namespace std;

int GCD(int x, int y) {
    if(x<y) {
        swap(x, y);
    }
    if(y==0) {
        return x;
    }
    return GCD(y, x%y);
}

int LCM(int x, int y) {
    return x/GCD(x, y)*y;
}

int main() {
    long long int N, M;
    cin >> N >> M;
    string S, T;
    cin >> S >> T;
    bool flag=true;
    for(long long int i=0; i<GCD(N, M); i++) {
        flag = (S[i*N/GCD(N, M)]==T[i*M/GCD(N, M)]);
        if(!flag) {
            break;
        }
    }

    if(flag) {
        cout << LCM(N, M) << endl;
    } else {
        cout << -1 << endl;
    }

    return 0;
    
}