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>

int gcd(int c,int b){
	if(b%c==0)return c;
	else return gcd(b,c%b);
}

int main(){
	int n,m;
	char s[100001];
	char t[100001];
	scanf("%d%d%s%s",&n,&m,s,t);
	int i,j;long l;
	if(n>m)l=m*n/gcd(m,n);
	else l=m*n/gcd(n,m);
	if(n==1||m==1){
		if(n==1){
			for(i=0;i<=m;i++){
				if(s[0]!=t[i]){
					puts("-1");
					return 0;
				}
			}
		}else
		if(m==1){
			for(i=0;i<=n;i++){
				if(s[i]!=t[0]){
					puts("-1");
					return 0;
				}
			}
		}
	}
	else{
		for(i=0;i<=n;i++){
			for(j=0;j<=m;j++){
				if(i*l/n==j*l/m){
//					printf("%d %d %c %c\n",i,j,s[i],t[j]);
					if(s[i*l/n]!=t[j*l/m]){
						puts("-1");
						return 0;
					}
				}
			}
		}
	}
	printf("%ld\n",l);
	return 0;
}