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.Collections.Generic;
public class ABC142D {
    private static List<long> primes = new List<long>();
    public static void Main() {
        long A, B, N = 1, ans = 0;
        string[] str = Console.ReadLine().Split(' ');
        A = long.Parse(str[0]);
        B = long.Parse(str[1]);

        N = Gozyohou(A, B);

        long i = 1;
        if (N % i == 0) {
            if (IsPrime(i)) ans++;
        }

        i = 2;
        if (N % i == 0) {
            while (N % i == 0) N /= i;
            if (IsPrime(i)) ans++;
        }

        i = 3;
        while (i <= N) {
            if (N % i == 0) {
                while (N % i == 0) N /= i;
                if (IsPrime(i)) ans++;
            }
            i += 2;
        }

        Console.WriteLine(ans);
    }

    private static bool IsPrime(long n) {
        for (int i = 1; i < primes.Count; i++) {
            if (n % primes[i] == 0) return false;
        }
        primes.Add(n);
        return true;
    }

    private static long Gozyohou(long A, long B) {
        long a = Math.Max(A, B);
        long b = Math.Min(A, B);
        long r = a % b;
        while (a % b != 0) {
            r = a % b;
            a = b;
            b = r;
        }
        return b;
    }
}