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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    long A = sc.nextLong();
    long B = sc.nextLong();
    long gcd = gcd(Math.max(A, B), Math.min(A, B));
    // count(prime <= gcd && gcd % prime == 0);
    int ans = 1; // include '1'.
    boolean[] isPrime = new boolean[1000_001 + 1];
    Arrays.fill(isPrime, true);
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i < isPrime.length; i++) {
      if (isPrime[i] && gcd % i == 0) {
        while(gcd % i == 0) {
          gcd /= i; // Assure uniqueness. e.g. 4=2*2*1
        }
        ans++;
      }
      for (int j = i; j < isPrime.length; j += i) {
        isPrime[j] = false;
      }
    }
    if (gcd > 1) ans++; // ?
    System.out.println(ans);
  }

  static long gcd(long a, long b) {
    if (b == 0) return a;
    return gcd(b, a % b);
  }
}