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 U(int x,int y){
	if(x>y){
		x=x-y;
		if(x==y){
			return x;
		}
		U(x,y);
	}else{
		y=y-x;
		if(x==y){
			return y;
		}
		U(x,y);
	}
}

int main(){
	int N,M,L,l;
	int flag=0;
	char S[100000],T[100000];
	int n,m,nm,n1,m1;
	int a,b,r,tmp;
	int i;
	scanf("%d%d",&N,&M);
	scanf("%s",S);
	scanf("%s",T);
	
	a=N;
	b=M;
	
	if(a<b){
		tmp = b;
		a = b;
		b = tmp;
	}
	
	r = a % b;
	while(r!=0){
		a = b;
		b = r;
		r = a % b;
	}
	l=r;

	
	L=N*M/l;
	n=N/l;
	m=M/l;
	
	
	n1=0;
	m1=0;
	
	
	for(;;){
		if(m1>=M){
			break;
		}
		
		if(n1>=N){
			break;
		}
		
		if(S[n1]==T[m1]){
			
		}else{
			flag=1;
			break;
		}
		n1=n1+n;
		m1=m1+m;
	}
	
	if(flag==0){
		printf("%d",L);
	}else{
		printf("-1");
	}
	
	return 0;
}