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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import kotlin.system.exitProcess

fun main(args: Array<String>) {
	val (n, m) = readLine()!!.split(' ').map { it.toInt() }
	val s = readLine()!!
	val t = readLine()!!

	val l = lcm(n, m)
	val arr = Array(l) { '-' }

	for ((i, c) in s.withIndex()) {
		val j = l / n * i
		arr[j] = c
	}

	for ((i, c) in t.withIndex()) {
		val j = l / m * i
		val v = arr[j]
		if (v != '-' && v != c) {
			println(-1)
			exitProcess(0)
		}
	}
	println(l)
}

fun gcd(a: Int, b: Int): Int {
	return when {
		a < b -> {
			gcd(b, a)
		}
		b == 0 -> {
			a
		}
		else -> {
			gcd(b, a % b)
		}
	}
}

fun lcm(a: Int, b: Int): Int {
	return (a * b) / gcd(a, b)
}