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: Wrong Answer)

import java.util.Scanner;

class Main{

	//static long[] a;
	static	int N ;
	static	int M ;
	static int[][] dp;

	static	boolean[] flag ;

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);			//文字の入力
		N = scanner.nextInt();
		M = scanner.nextInt();

		long ans = lcm(N, M);

		String s = scanner.next();
		String t = scanner.next();

		int sl = s.length();
		int tl = t.length();

		StringBuilder sb = new StringBuilder();
		
		int c = 0;

		if(N >= M){

			for(int i = 0;i < (sl-1)*ans/N;i++){
				if(i == 0 || i % (ans/N) == 0 ){
					sb.append(s.substring(c, c+1));
					c++;
				}else{
					sb.append("1");
				}
			
			}
//			System.out.println("ans "+ans);

			String aa = sb.toString();
//			System.out.println(aa);
			
			c= 0;
			for(int i = 0;i < (tl-1)*ans/M;i++){

				if(i == 0 || i % (ans/M) == 0){
//					System.out.println("i "+i);
//					System.out.println(aa.substring(i,i+1) );


					if(!(aa.substring(i,i+1).equals(t.substring(c, c+1))) && !(aa.substring(i,i+1).equals("1")) ){
						System.out.println("-1");
						return;
					}
					c++;
				}
				
			}
			
		}else{

			for(int i = 0;i < (tl-1)*ans/M;i++){
				if(i == 0 || i % (ans/M) == 0 ){
					sb.append(t.substring(c, c+1));
					c++;
				}else{
					sb.append("1");
				}
			
			}
//			System.out.println("ans "+ans);

			String aa = sb.toString();
//			System.out.println(aa);
			
			c= 0;
			for(int i = 0;i < (sl-1)*ans/N;i++){

				if(i == 0 || i % (ans/N) == 0){
//					System.out.println("i "+i);
//					System.out.println(aa.substring(i,i+1) );


					if(!(aa.substring(i,i+1).equals(s.substring(c, c+1))) && !(aa.substring(i,i+1).equals("1")) ){
						System.out.println("-1");
						return;
					}
					c++;
				}
				
			}
			
			
		}
		
		System.out.println(ans);
		





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