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 scala.io.StdIn

object Main extends App {
  val Array(a, b) = StdIn.readLine().split(" ").map(_.toLong)
  val gcd_v = gcd(a, b)

  println(primeDivSize(gcd_v))
  

  def isPrime(i: Long) : Boolean = {
    if (i == 2l)
      true
    else
      !(2l to (i-1l)).exists(x => i % x == 0l)
  }

  def primeDivSize(i: Long) : Int = {
    val range :Long = Math.sqrt(i).ceil.toLong
    var target = i
    val ans :scala.collection.mutable.Set[Long] = scala.collection.mutable.Set[Long](1)
    var j = 2
    while (j <= range) {
      if (target % j == 0) {
        ans += j
        target = target / j }
      else j = j + 1
    }

    if (target != 1) ans += target

    ans.size
  }
  
  def gcd(a: Long,b: Long): Long = {
    if(b ==0l) a  else gcd(b, a%b)
  }
}