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 <bits/stdc++.h>

using namespace std;

typedef unsigned int ui;
typedef long long ll;
typedef unsigned long long ull;

constexpr int MAXNM = 100000;

char S[MAXNM + 2], T[MAXNM + 2];

int main() {
	int N, M;
	cin >> N >> M;
	if(N > M) {
		swap(N, M);
		cin >> T >> S;
	} else {
		cin >> S >> T;
	}
	if(M % N == 0)
		for(int i = 0, j = 0; i < N; i++, j += M / N)
			if(S[i] != T[j])
				goto imp;
	if(S[0] != T[0])
		goto imp;
	cout << ((ll)N * M / __gcd(N, M)) << endl;
	return 0;
imp:
	cout << -1 << endl;
}