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: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<math.h>
int gcd(int a,int b){
	if (a < b) {
		int tmp = a;
		a = b;
		b = tmp;
}
	int r=a%b;
	
	while (r != 0) {
		a = b;
		b = r;
		r = a % b;

	}
	return b;
}


int main(){
	int c,n, m,i,cnt=0;
	char s[100001], t[100001];
	scanf("%d%d", &n, &m);
	scanf("%s%s", s, t);
	c = gcd(n, m);
	for (i = 0;i<c;i++) {
		if (s[(n / c)*i] == t[(m / c)*i])
			cnt++;
	}
	if (cnt == c)printf("%lld", (n*m) / c);
	else printf("%d", -1);
		return 0;
}