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: Wrong Answer)

#include <iostream>
#include <string>
using namespace std;

int gcd(int a,int b){
    if(a<b){
        int temp=a;
        a=b;
        b=temp;}
    if(b==0)
        return a;
    int c=a%b;
    return gcd(b,c);}

int lcm(int x,int y){
    return int((x*y)/gcd(x, y));}

int cal(string S,string T,int N,int M){
    int L=lcm(N,M);
    int index=0;
    int s[N]={};
    for(int i=0;i<N;i++){
        s[index]=i*(L/N);
        index++;}
    for(int i=0;i<M;i++){
        int r=i*(L/M);
        for(int j=0;j<index;j++){
            if(r==s[j]){
                if(S[i]!=T[j])
                    return -1;}
            if(r<s[j]) continue;}}
            
    return L;}

int main(){
string S,T;
int N,M;
cin>>N>>M;
cin>>S;
cin>>T;
cout<<cal(S,T,N,M);
}