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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        String s = in.next();
        String t = in.next();

        int l = Math.max(n, m);
        while(true) {
            if(l % n != 0 || l % m != 0) {
                l++;
            } else {
                break;
            }
        }

        if(l == Math.max(n, m)) {
            System.out.println(-1);
            return;
        }

        boolean flag = true;
        int ln = l / n;
        int lm = l / m;
        char[] x = new char[l];

        for(int i=0; i<l; i++) x[i] = '-';

        for(int i=0; i<n; i++) {
            int d = i * ln + 1 - 1;
            char sc = s.charAt(i);
            x[d] = sc;
        }

        for(int i=0; i<m; i++) {
            int e = i * lm + 1 - 1;
            char tc = t.charAt(i);
            if(x[e] == '-' || x[e] == tc) {
                x[e] = tc;
            } else {
                flag = false;
                break;
            }
        }

        if(flag) {
            System.out.println(l);
        } else {
            System.out.println(-1);
        }
    }
}