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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function toNum(str) {
	return parseInt(str, 10);
}

// 最大公約数
function gcd(a, b) {
	if (a % b === 0) {
		return b;
	} else {
		return gcd(b, a % b);
	}
}

// 最小公倍数
function lcm(a, b) {
	return a * b / gcd(a, b);
}

// inputに入力データ全体が入る
function Main(input) {
	var N = toNum(input.split('\n')[0].split(' ')[0]);
	var M = toNum(input.split('\n')[0].split(' ')[1]);
	var S = input.split('\n')[1];
	var T = input.split('\n')[2];
	var L = N > M ? lcm(N, M) : lcm (M, N);
	var flag = true;
	var X = [];
	for ( var i = 0; i < L; i++) {
		X.push('');
	}
	X[0] = S[0];
	for ( var i = 1; i < S.length; i++ ) {
		X[i * (L / N)] = S[i];
	}
	if ( X[0] != T[0] ) {
		console.log('-1');
	} else {
		for (var i = 1; i < T.length; i++) {
			if (X[i * (L / M)] != '' && X[i * (L / M)] != T[i]) {
				console.log('-1');
				flag = false;
				break;
			}
		}
	}
	if ( flag ) {
		console.log(L);
	}
}

// ※この行以降は編集しない (標準入力から一度に読み込みMainを呼び出します)
Main(require("fs").readFileSync("/dev/stdin", "utf8"));