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: Accepted)

#include <bits/stdc++.h>
using namespace std;

long long gcd(long long a, long long b){
	if (b == 0) return a;
	return gcd(b, a % b);
}
 
long long lcm(long long a, long long b){
	if (b > a) swap(a, b);
	return a / gcd(a, b) * b;
}



int main(){
	int N,M;
	cin>>N>>M;
	long long x = lcm((long long)N,(long long)M);
	string S,T;
	cin>>S>>T;

	for(long long i=0;i<x;i+=x/N){
		if(i%(x/M)!=0)continue;
		char a = S[i/(x/N)];
		char b = T[i/(x/M)];
		if(a!=b){
			cout<<-1<<endl;
			return 0;
		}
	}
	cout<<x<<endl;
			
	
	
	return 0;
}