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++14 (GCC 5.4.1) (judge verdict: Accepted)

//https://agc028.contest.atcoder.jp/tasks/agc028_a
#include<cstdio>
using namespace std;
char s[100005],t[100005];
int tmp,n,m,i,j,pos1,pos2;
int gcd(int a,int b){return b==0?a:gcd(b,a%b);} 
int main()
{
	scanf("%d%d%s%s",&n,&m,s,t);
	tmp=gcd(n,m);
	pos1=0;pos2=0;
	for(i=0;i<tmp;i++,pos1+=n/tmp,pos2+=m/tmp)
	{
		if(s[pos1]!=t[pos2])
		{
			printf("-1");
			return 0;
		}
	}
	printf("%lld\n",1LL*n*m/tmp);
	return 0;
}