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)

object Main {
  def main(args:Array[String]) {
    val ab = readLine().split(' ').map(_.toLong)
    var g:Long = gcd(ab(1), ab(0))
    var ans = 1
    var loop = math.sqrt(g).toLong + 1
    for(i <- 2l to loop) {
      var flag = false
      while(g % i == 0) {
        flag = true
        g /= i
      }
      if(flag) ans += 1
    }
    if(g != 1) ans += 1
    println(ans)
  }

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