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 yaku(int a, int b){
    if(a>b) return yaku(b,a);
    else{
        if(b%a==0) return a;
        else return yaku(b%a,a);
    }
}

int main(){
    int N,M;
    string S,T;
    cin>>N>>M>>S>>T;

    if (S.at(0)!=T.at(0)) cout<<"-1"<<endl;
    else{
        int y=yaku(N,M);
        if(y==1) cout<<N*M<<endl;

        else{
            int ans=N*M/y;
            int n=ans/N;
            int m=ans/M;
            int d=ans/y;
            bool p=true;
            for(int i=0;i<N;i+=d){
                if (S.at(i/n)!=T.at(i/m)){
                    p=false;
                    cout<<"-1"<<endl;
                    break;
                }
            }
            if(p) cout<<ans<<endl;
        }
    }
}