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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Contest {
  static void Main() {
    var input = Console.ReadLine().Trim().Split(' ').Select(x => long.Parse(x)).ToArray();
    long A = input[0];
    long B = input[1];
    List<long> candidate = new List<long>();
    
    var C = A > B ? A : B;
    for(long i = 1; i <= C; i++) {
      if(A % i == 0 && B % i == 0 && something(i, candidate)) {
        candidate.Add(i);
      }
    }

    //Console.WriteLine(string.Join(" ", candidate));
    Console.WriteLine(candidate.Count());
    
    /*
    int count = 0;
    for(var i = 0; i < candidate.Count(); i++) {
      for(var j = i + 1; j < candidate.Count(); j++) {
        var x = candidate[i];
        var y = candidate[j];
        if(gcd(x, y) == 1) {
          Console.WriteLine("x: " + x + " y: " + y);
          count++;
        }
      }
    }
    
    Console.WriteLine(count);    
    */
    
  }
  
  static private int gcd(int a, int b) {
      return b >= 1 ? gcd(b,a % b) : a;
  }
  
  static private bool something(long a, List<long>l) {
    for(var i = 0; i < l.Count(); i++) {
      if(l[i] == 1) {
        continue;
      }
      if(a % l[i] == 0) {
        return false;
      }
    }
    return true;
  }
}