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 <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
//　とりあえず読み込む
using namespace std;

int main() {
  int N, M;
  cin >> N >> M;
  string S, T;
  cin >> S;
  cin >> T;
  if (S[0] != T[0]) {
    cout << "-1" << endl;
    return 0;
  }
  int n1, n2;
  if (N > M) {
    n1 = N;
    n2 = M;
  } else {
    n1 = M;
    n2 = N;
  }
  int lcm = 0;
  int gcf = 0;
  for (int i = 1; i <= 100000; ++i) {
    if ((i * n1) % n2 == 0) {
      lcm = i * n1;
      gcf = n2 / i;
      break;
    }
  }
  assert(lcm != 0 && gcf != 0);
  for (int i = 1; i < gcf; ++i) {
    if (S[N/gcf*i] != T[M/gcf*i]) {
      cout << "-1" << endl;
      return 0;
    }
  }
  cout << lcm << endl;
  return 0;
}