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<string>
using namespace std;

bool hantei(string a,string b,int kaisuu){
	string aa;
	for(int i=0;i<kaisuu;i++){
		aa=a+aa;
	}
	if(aa==b){
		return b.length();
	}else{
		return -1;
	}
}


//x<yとする
int mod(int x,int y,string a,string b,bool z){
	if(y%x==0){
		if(z==false){
			return hantei(a,b,y/x);
		}else{
			return x*y;
		}
	}else{
		mod(y%x,x,b,a,true)*x;
	}
}

main(){
	int x,y;
	string a,b;
	cin >> x >> y;
	cin >> a;
	cin >> b;

	if(x<y){
		cout << mod(x,y,a,b,false) <<endl;
	}else{
		cout << mod(y,x,b,a,false) <<endl;
	}

}