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{
  def main(args:Array[String]):Unit={
    var MN = readLine
    var S = readLine
    var T = readLine
    var res = new calculate(S,T)
   
    println(res.calculate())

  }
}

import scala.collection.mutable.ArrayBuffer

class calculate(s:String,t:String){
  var lens = s.length
  var lent = t.length

   def calculate():Int={
    var lcm = getLCM()
    var res = lcm

    var record:Map[Int,String] = Map()

    for(i <- 0 until lens){
      var temp = i*(lcm/lens)+1
      record += (temp -> s.charAt(i).toString)
    }
    var flag = true
    for(i <- 0 until lent if flag){
      var temp = i*(lcm/lent)+1
      var tempRecord = record.getOrElse(temp,"0")
      if(!tempRecord.equals("0") && !tempRecord.equals(t.charAt(i).toString)){
        flag = false
        res = -1
      }
    }
    res
  }



  def getLCM():Int={
    return lens*lent/getGCD
  }

  def getGCD():Int={
    var tempN = lens
    var tempM = lent
    var c = lens % lent
    while(c!=0){
      tempN = tempM
      tempM = c
      c = tempN % tempM
    }
    return tempM
  }
}