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)

object Main extends App {
  import scala.io.StdIn._


  val Array(n, m) = readLine.trim.split(' ').map(_.toInt)
  val s = readLine.trim
  val t = readLine.trim
  val g = gcd(n, m)
  val (a, b) = (n / g, m / g)
  println(
    if ((0 until g).forall(y ⇒ s(y * a) == t(y * b))){
      a * b * g
    }else {
      -1
    }
  )
  def gcd(a:Int, b:Int):Int = {
    b match {
      case 0 ⇒ a
      case _ ⇒ gcd(b, a % b)
    }
  }
  implicit class ScopeFunc[T](val value: T){
    def let[A](func: T ⇒ A): A = func(value)
    def also(func: T ⇒ Unit): T = {
      func(value)
      value
    }
  }
}