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

int main(){
  int n,m;
  cin >> n>>m;
  string s;
  string t;
  cin >> s>>t;
  int gcd=gccal(max(n,m),min(n,m));
  int lcm=n/gcd*m;
  for(int i=1;i<100000;i++){
    long l=i*lcm;
    bool ans=true;
    string u(i*lcm,'0');
    for(int j=0;j<n;j++){
      u.at(-1+j*l/n+1)=s.at(j);
    }
    for(int j=0;j<m;j++){
      if(u.at(-1+j*l/m+1)!=t.at(j)&&u.at(-1+j*l/m+1)!='0'){
        ans=false;
        break;
      }
    }
    if(ans){
      cout << l;
      return 0;
    }
  }
  cout << -1;
           
      
}