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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
int gcd(int a,int b){
   if(a%b==0){
      return b;
   }else{
      return gcd(b,a%b);
   }
}
int main(void){
   int N,M;
   cin>>N>>M;
   string S,T;
   cin>>S>>T;
   long long result=N*M/gcd(N,M);
   vector<char> ans(result,'a');
   for(int i=0;i<N;i++){
      ans[i*(result/N)]=S[i];
   }
   for(int i=0;i<M;i++){
      ans[i*(result/M)]=T[i];
   }
   
   bool flag=true;
   for(int i=0;i<N;i++){
      if(ans[i*(result/N)]!=S[i]){
         flag=false;
         break;
      }
   }
   for(int i=0;i<M;i++){
      if(ans[i*(result/M)]!=T[i]){
         flag=false;
         break;
      }
   }
   if(flag) cout<<result<<endl;
   else cout<<-1<<endl;
   return 0;
}