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;
class ProgramD
    {
        static void Main(string[] args)
        {

            string[] input = Console.ReadLine().Split(' ');

            ulong a = ulong.Parse(input[0]);
            ulong b = ulong.Parse(input[1]);

            if(a < b)
            {
                ulong tmp = a;
                a = b;
                b = tmp;
            }
            ulong r = a % b;
            while(r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }

            ulong c = b;
            ulong d = b;
            ulong count = 1;
            int frag = 0;

            for(ulong i = 2; i <= Math.Sqrt(c); i++)
            {
                while(c % i == 0)
                {
                    c /= i;
                    frag = 1;
                }

                if(frag == 1)
                {
                    count++;
                    frag = 0;
                }  

            }
            
            if(c != 1)
                count++;
          
            if(d == 1)
                count = 1;

            Console.WriteLine(count);
        }


        }