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: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<string>
using namespace std;
int main(){
	int m,n;
	string a,b;
	cin>>m>>n;
	cin>>a>>b;
	int m1=m,n1=n,q;
	q=m1%n1;
	if(m1<n1){
		int h=m1;
		m1=n1;
		n1=h;
	}
	while(q!=0){
		m1=n1;
		n1=q;
		q=m1%n1;
	}
	int t=m*n/n1;
	int aa=(n-1)*t/n+1;
	int bb=(m-1)*t/m+1;
	if(aa<bb){
		aa=bb;
	}
	if(aa>=t){
		cout<<-1<<endl;
	}else{
		cout<<t<<endl;	
	}
}