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: Runtime Error)

import java.io.*;
import java.util.*;

public class Main {
    static class Writer {
        PrintWriter cout;

        Writer() throws IOException {
            cout = new PrintWriter(System.out);
        }

        Writer(String name) throws IOException {
            cout = new PrintWriter(new FileWriter(name));
        }

        StringBuilder out = new StringBuilder();

        void print(Object a) {
            out.append(a);
        }

        void close() {
            cout.print(out.toString());
            cout.close();
        }
    }

    static class Reader {
        BufferedReader in;

        Reader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        Reader(String name) throws IOException {
            in = new BufferedReader(new FileReader(name));
        }

        StringTokenizer tokin = new StringTokenizer("");

        String next() throws IOException {
            if (!tokin.hasMoreTokens()) {
                tokin = new StringTokenizer(in.readLine());
            }
            return tokin.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }


    static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    public static void main(String args[]) throws IOException {
        Reader in = new Reader();
        Writer out = new Writer();
        int n = in.nextInt();
        int m = in.nextInt();
        String s = in.next();
        String t = in.next();
        int lsp = (n * m) / gcd(n, m);
        int lss = lsp / n;
        int lst = lsp / m;
        char X[] = new char[lsp];
        boolean must = true;
        for (int i = 0; i < n; i++) {
            X[i * lss] = s.charAt(i);
        }
        for (int i = 0; i < m; i++) {
            if (X[i * lst] == 0) {
                X[i * lst] = t.charAt(i);
            } else {
                if (X[i * lst] != t.charAt(i)) {
                    must = false;
                    break;
                }
            }
        }
        if (must) {
            out.print(lsp);
        } else {
            out.print("-1");
        }
        out.close();
    }
}