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 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

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

int main()
{
	int N, M;
	char S[100001], T[100001];
	scanf("%d %d", &N, &M);
	scanf("%s", S);
	scanf("%s", T);
	
	int i, j, G = gcd(N, M), L = N / G * M, n = L / N, m = L / M, flag = 1;
	for (i = 0, j = 0; i < N && j < M; i += m, j += n) {
		if (S[i] != T[j]) flag = 0;
	}
	
	if (flag == 1) printf("%d\n", L);
	else printf("-1\n");
	fflush(stdout);
	return 0;
}