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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    //最小公倍数lcm
    static int lcm (int a, int b) {
    	int temp;
    	long c = a;
    	c *= b;
    	while((temp = a%b)!=0) {
    		a = b;
    		b = temp;
    	}
    	return (int)(c/b);
    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int LCM = lcm(N,M);//N,Mの最小公倍数
        int LN = LCM/N;
        int LM = LCM/M;
        int lcmOflcm =lcm(LN,LM);
        int result = LCM;
        String S = sc.next();
        String T = sc.next();
        int LB = LCM/lcmOflcm;
        for(int i = 0; i < LB; i++){
            if(!(S.substring(N/LB*i,N/LB*i+1).equals(T.substring(M/LB*i,M/LB*i+1)))){
                result = -1;
            }
        }
        System.out.println(result);
    }
}