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: Accepted)

#include<iostream>
#include<math.h>
#include<stdio.h>
#include<vector>
#include<string>
#include<algorithm>
#include<numeric>
#include<cmath>

using namespace std;

long long int A, a, n, m, y, s;
string str_1, str_2, str_3;


long long int gcd(int m, int n){
	while (true) {
		if (m%n == 0)return n;
		m %= n;
		if (n%m == 0)return m;
		n %= m;
	}
}



int main() {
	cin >> n >> m;
	cin >> str_1 >> str_2;

	y = gcd(n, m);

	for (int i = 0; i < y; i++) {
		if (str_1[i*n / y] != str_2[i*m / y]) {
			cout << -1 << '\n';
			return 0;
		}
	}
	cout << n * m / y << '\n';
	return 0;
}