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.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/*
 * AtCoder Grand Contest 028 A "Two Abbreviations"
 *   https://agc028.contest.atcoder.jp/tasks/agc028_a/
 */
public class Main {

	public static void main(String[] args) {

		InputScanner in = new InputScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		Task task = new Task();
		task.run(in, out);

		in.close();
		out.close();
	}

	static class Task {

		public void run(InputScanner in, PrintWriter out) {

			int N = in.nextInt();
			int M = in.nextInt();
			String S = in.next();
			String T = in.next();

			int lcm = (int) lcm(N, M);

			int ans = -1;
			for (int L = lcm; L <= lcm; L += lcm) {

				boolean ans2 = true;
				int lcm2 = (int) lcm(L / N, L / M);
				for (int i = 0; i < Math.min(N, M); i += lcm2) {
					int si = i / (L / N);
					int ti = i / (L / M);
					if (S.charAt(si) != T.charAt(ti)) {
						ans2 = false;
						break;
					}
				}

				if (ans2) {
					ans = L;
					break;
				}
			}

			out.println(ans);
		}

	}

	private static long lcm(long m, long n) {
	    return m * n / gcd(m, n);
	}

	private static long gcd(long m, long n) {
	    if(m < n) return gcd(n, m);
	    if(n == 0) return m;
	    return gcd(n, m % n);
	}

	/*
	 * extends java.util.Scanner
	 */
	static class InputScanner {

		Scanner scanner;

		public InputScanner(InputStream inputStream) {
			this.scanner = new Scanner(inputStream);
		}

		public boolean hasNext() {
			return scanner.hasNext();
		}

		public int nextInt() {
			return Integer.parseInt(scanner.next());
		}

		public long nextLong() {
			return Long.parseLong(scanner.next());
		}

		public double nextDouble() {
			return Double.parseDouble(scanner.next());
		}
		public String next() {
			return scanner.next();
		}

		public int[] nextIntArray(int n) {
			int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = scanner.nextInt();
			}
			return ret;
		}

		public int[][] nextIntArray(int h, int w) {
			int[][] ret = new int[h][w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					ret[i][j] = scanner.nextInt();
				}
			}
			return ret;
		}

		public long[] nextLongArray(int n) {
			long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = scanner.nextLong();
			}
			return ret;
		}

		public long[][] nextlongArray(int h, int w) {
			long[][] ret = new long[h][w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					ret[i][j] = scanner.nextLong();
				}
			}
			return ret;
		}

		public double[] nextDoubleArray(int n) {
			double[] ret = new double[n];
			for (int i = 0; i < n; i++) {
				ret[i] = scanner.nextDouble();
			}
			return ret;
		}

		public double[][] nextDoubleArray(int h, int w) {
			double[][] ret = new double[h][w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					ret[i][j] = scanner.nextLong();
				}
			}
			return ret;
		}

		public String[] nextStringArray(int n) {
			String[] ret = new String[n];
			for (int i = 0; i < n; i++) {
				ret[i] = scanner.next();
			}
			return ret;
		}

		public String[] nextStringArray(String split) {
			String[] ret = scanner.next().split(split);
			return ret;
		}

		public String[][] nextStringArray(int h, int w) {
			String[][] ret = new String[h][w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					ret[i][j] = scanner.next();
				}
			}
			return ret;
		}

		public String[][] nextStringArray(int h, String split) {
			String[][] ret = new String[h][];
			for (int i = 0; i < h; i++) {
				ret[i] = scanner.next().split(split);
			}
			return ret;
		}

		public void close() {
			scanner.close();
		}

	}

}