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)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define vecll vector<long long>
#define vec2ll vector<vector<long long>>
#define vecpairll vector<pair<long long,long long>>
#define forll(s,a,b) for(long long s = a;s < b;s++)
#define forllde(s,a) for(long long s = a;s > 0;s--)


ll gcd(ll a,ll b){
  if(a<b)swap(a,b);
  if(a%b==0)return b;
  return gcd(a%b,b);
}

ll lcm(ll a,ll b){
  return a/gcd(a,b)*b;
}


int main()
{
  ll n, m, lcmnm;
  cin >> n >> m;
  string s, t;
  cin >> s >> t;
  lcmnm = lcm(n, m);
  forll(i, 0, m){
	if (n * i % m == 0){
	  if (t[i] != s[i * n / m]){
		cout << -1 << endl;
		return 0;
	  }
	}
  }
  cout << lcmnm << endl;
}