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)

/// awoooooo

# include <bits/stdc++.h>
# define sz(x) (int)((x).size())

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair < int, int > pii;
typedef complex < ld > point;

const int N = (int)2e5 + 5;
const int inf = (int)1e9 + 7;

int n, m;
string a, b;
map < int, char > c;

int main(){
  cin >> n >> m >> a >> b;
  ll l = n * 1ll * m / __gcd(n, m);
  for(ll i = 1, e = 0; e < n; i += l / n, ++e){
    c[i] = a[e];
  }
  for(ll i = 1, e = 0; e < m; i += l / m, ++e){
    if(c.count(i) && c[i] != b[e]){
      cout << "-1\n";
      return 0;
    }
  }
  cout << l << "\n";
  return 0;
}