Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main extends App{
  val sc = new Scanner(System.in)

  val a = sc.nextLong
  val b = sc.nextLong

  val g = gcd(a,b)
  val sqrtG = Math.sqrt(g).ceil.toLong

  val res =
    g match {
      case 1 => 1
      case 2 => 2
      case 3 => 2
      case gg => {
        val temp = loop( (gg, Vector(1), 2) )._2
        temp.size
      }
    }

  println(res)


  def gcd(a: Long, b: Long): Long ={
    (a,b) match{
      case (x,y) if y == 0 => x
      case (x,y) if x < y  => gcd(y, x)
      case (x,y)           => gcd(y, x % y)
    }
  }

  def loop( tuple: (Long, Vector[Long], Long)): (Long, Vector[Long], Long) = {
    val (n, vec, diviser) = tuple
    if( n == 1 ) {
      (n, vec, diviser)
    } else if (diviser > sqrtG){
      (n, vec :+ n, diviser)
    }    else {
      def divLoop(num: Long, d: Long): Long =
        if(num % d != 0) num else divLoop(num / d, d)

      val newN = divLoop(n, diviser)
      val newVec = if(newN == n) vec else vec :+ diviser

      loop((newN, newVec, diviser + 1))
    }
  }



}