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 gcd(a, b) {
    if (b === 0){
        return a
	}
    return gcd(b, a % b)
}

function get_indexs(n,l){
	var array = []
	array.push(0)

	for (var i = 1; i <= n - 1; i++) {
		array.push((i*l)/n)
	}
	return array
}


function main(arg) {
	var arg = arg.split("\n")
	var tmp = arg[0].split(" ")
	var n = Number(tmp[0])
	var m = Number(tmp[1])
	var s = arg[1]
	var t = arg[2]
	var k = gcd(n,m)

	if (n%m === 0 || m%n === 0) {
		console.log(-1)
		return
	}

	var _n = n/k
	var _m = m/k

	if (_n % _m === 0 || _m % _n === 0) {
		console.log(-1)
		return
	}


	var i = 0

	for (i = n*m/k; i < Math.pow(10,5); i+=(n*m/k)) {
		var n_arr = get_indexs(n, i)
		var m_arr = get_indexs(m, i)
		var flg = true

		for (var j = 0; j < i; j++) {
			var n_i = n_arr.indexOf(j)
			var m_i = m_arr.indexOf(j)

			if (n_i < 0 || m_i < 0) {
				continue
			}

			if (s[n_i] !== t[m_i]) {
				flg = false
				break
			}
		}

		if (flg) {
			break
		}
	}
	console.log(i)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));