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 <stdbool.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
typedef long long int ll;
#define mod 1000000007
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define m0(x) memset(x,0,sizeof(x))

int gcd(ll a,ll b){
	ll 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;
}

int lcm(ll a,ll b){
	return a*b/gcd(a,b);
}


int main(void){
	ll n,m,o,p;
	scanf("%lld %lld",&n,&m);
	char s[n],t[m];
	scanf("%s",s);
	scanf("%s",t);
	o=lcm(n,m);
	ll flag=0;
	p=lcm(o/n,o/m);
	ll on,om;
	for(ll i=0; i<o; i=i+p){
		on=i/(long double)o*n;
		om=i/(long double)o*m;
		if(s[on]==t[om]){}
		else flag++;
	}
	if(flag!=0) printf("-1");
	else printf("%lld",o );

	return 0;
}