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 <stdlib.h>

#define MAX 100000
int GCD(int ,int);

int main(void){
	
	long long int N,M,G,i,n,m;
	char *S,*T;
  
	scanf("%lld %lld",&N,&M);
  	if(N > MAX || M > MAX){
		return 0;    
    }
	S = (char *)malloc((N+1)*sizeof(char));
	T = (char *)malloc((M+1)*sizeof(char));
	scanf("%s",S);
	scanf("%s",T);

	G = GCD(N,M);
  	n = N/G;
  	m = M/G;

	for(i=0;i<G;i++){
    	if(S[i*n] != T[i*m]){
 			printf("-1\n");       	
			free(S);
			free(T);
			return 0;
        }
    }
  
	printf("%lld\n",(long long int)(N/G*M));

	free(S);
	free(T);
	return 0;
}


int GCD(int a,int b){
	
	int tmp,r;
	
	if(a<b){
		tmp = a;
		a = b;
		b = tmp;
	}
	
	r = a % b;
	
	while(r != 0){
		a = b;
		b = r;
		r = a % b;
	}
  	return b;

}