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: Accepted)

#include <stdio.h>
#include <string.h>

long gcd(long x, long y)
{
	return y ? gcd(y, x % y) : x;
}

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

int main(void)
{
	char S[100001], T[100001];
	long N, M, Slength, Tlength, min, tmp, i;
	scanf("%ld%ld%s%s", &N, &M, S, T);
	Slength = strlen(S);
	Tlength = strlen(T);
	tmp = lcm(N, M);
	//if (Slength / (tmp / N) < Tlength / (tmp / M)) min = Slength / (tmp / N);
	//else min = Tlength / (tmp / M);

	long LCM = lcm(tmp / N, tmp / M);

	for (i = 0; S[i / (tmp / N)] != '\0' && T[i / (tmp / M)] != '\0'; i += LCM) {
		if (S[i / (tmp / N)] != T[i / (tmp / M)]) {
			puts("-1");
			return 0;
		}
	}
	printf("%ld", tmp);
	return 0;
}