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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.StdIn._
object Main extends App {
  def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
  def lcm(a: Int, b: Int): Int = a * b / gcd(a, b)

  val Array(sl, tl) = readLine.split(" ").map{_.toInt}
  val s, t = readLine
  val lcmValue= lcm(sl, tl)

  def judge(xl: Int): Boolean = {
    val sChars = (0 until sl).map{i => (xl / sl * i + 1, s.charAt(i))}
    val tChars = (0 until tl).map{i => (xl / tl * i + 1, t.charAt(i))}.toMap
    sChars.forall{case (i, sc) => tChars.get(i).fold(true){tc => sc == tc}}
  }

  val result: Int =
    if (lcmValue % sl == 0 || lcmValue % tl == 0) {
      if (judge(lcmValue)) lcmValue
      else -1
    } else (lcmValue to (sl * tl) by lcmValue).find(judge).getOrElse(-1)
  println(result)
}