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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

int gcd(int a, int b){
	if(b==0) return a;
	return(b,a%b);
}

int main(){

	int n,m;
	string s,t;
	cin >> n >> m >> s >> t;
	int g = gcd(n,m);
	int l = (long long) (n*m)/g;
	if(l==max(m,n)){
		cout << l;
		return 0;
	}else{
		if(n>m){
			for(int i=0;i<m;i++){
				if(t[i]!=s[i*(l/m)]){
					cout << -1;
					return 0;
				}
			}
		}else{
			for(int i=0;i<n;i++){
				if(s[i]!=t[i*(l/n)]){
					cout << -1;
					return 0;
				}
			}
		}
	}
	cout << l;
}