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: Accepted)

using System;
using System.Collections.Generic;

class ABC_142_D
{
    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split(' ');
        long A = long.Parse(input[0]);
        long B = long.Parse(input[1]);

        long gcd = GCD(A, B);
        List<long> Div = new List<long>();
        Div.Add(1);

        long c = gcd;
        double limit = Math.Sqrt(c);

        if (c%2==0) Div.Add(2);
        while (c%2==0) c/=2;

        long d = 3;
        while (c>1)
        {
            if(c%d==0)
            {
                Div.Add(d);
                while(c%d==0) c/=d;
            }

            d+=2;

            if (limit < d)
            {
                if(!Div.Contains(c)) Div.Add(c);
                break;
            }
        }

        Console.WriteLine(Div.Count);
    }

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