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: Time Limit Exceeded)

import java.util.*;
public class Main{   
    public static void main(String[] args){
      Scanner sc = new Scanner(System.in);
      long a = sc.nextLong();
      long b = sc.nextLong();
      long g = gcd(a,b);
      long cnt = 1;
      boolean f = true;
      for(long i = 2;i <= g;i++){
      	for(long j = 2;j < i;j++)if(i%j==0)f = false;
        if(f&&g%i==0)cnt++;
        f = true;
      }
      System.out.println(cnt);
    }
    
    public static long gcd(long x, long y){
      if(x < y)return gcd(y,x);
      if(y==0)return x;
      return gcd(y,x%y);
    }
}