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;
using System.Linq;

namespace ABC142D
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            long[] ab = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            long gcd = Gcd(ab[0], ab[1]);
            var primes = FactorizePrimes(gcd);
            Console.WriteLine(primes.Distinct().Count() + 1);
        }

        public static long Gcd(long a, long b)
        {
            Func<long, long, long> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }

        static IEnumerable<long> FactorizePrimes(long n)
        {
            long i = 2;
            long temp = n;
            while (i < Math.Sqrt(n))
            {
                if (temp % i == 0)
                {
                    temp /= i;
                    yield return i;
                }
                else i++;
            }
            if (temp != 1) yield return temp;
        }
    }
}