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: Accepted)

fun gcd(x: Int, y: Int): Int {
  if (x < y) {
    return gcd(y, x)
  }
  val r = x % y
  if (r == 0) {
    return y
  } else {
    return gcd(y, r)
  }
}

fun main(args: Array<String>) {
  val (n, m) = readLine()!!.split(" ").map { it.toInt() }
  val s = readLine()!!
  val t = readLine()!!
  val r = gcd(n, m)
  for (k in 0 until r) {
    if (s[k * (n / r)] != t[k * (m / r)]) {
      println(-1)
      return
    }
  }
  println(n.toLong() * m.toLong() / r.toLong())
}