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 int gcd(long int a, long int b) {
	int big, small;
	if (a < b)big = b, small = a;
	else big = a, small = b;
	if (big % small == 0)return small;
	else return gcd(small, big % small);
}

int main(void) {
	long int n, m,lcm,g,i,ok = 1;
	char nn[100001], mm[100001];

	scanf("%d %d", &n, &m);
	scanf("%s", nn);
	scanf("%s", mm);
	g = gcd(n, m);
	lcm = n * m / g;

	for (i = 0; i < g; i++) {
		if (nn[n * i / g] != mm[m * i / g]) {
			ok--;
			break;
		}
	}

	if (ok) {
		printf("%ld\n", lcm);
	}
	else {
		printf("-1\n");
	}

}