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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp18 {
    class Program {
        static void Main(string[] args) {
            var x = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

            long A = x[0];
            long B = x[1];

            long gcd = Gcd(A, B);

            int ans = 1;

            //gcdの約数の中で、素数をカウントする
            for (int i = 2; i <= gcd / 2; i++) {
                if (isPrime(i) && gcd % i == 0) {
                    //Console.WriteLine(i);
                    ans++;
                }
            }

            Console.WriteLine(ans);
        }

        public static bool isPrime(int a) { 
            for (int i = 2; i <= Math.Sqrt(a); i++) {
                if (a % i == 0) {
                    return false;
                }
            }
            return true;
        }

        public static long Gcd(long a, long b) {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0) {
                long remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }
    }
}