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: Runtime Error)

using System;

class Program {
    static void Main(string[] args) {

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

        long a = int.Parse(ab[0]);
        long b = int.Parse(ab[1]);

        long min = a;
        if (a > b) min = b;

        long result = 0;

        for (int num = 1; num <= min / 2; num++) {
            if (a % num == 0 && b % num == 0) {
                bool tf = true;
                for(int num2 = 2; num2 < num; num2++) {
                    if (num % num2==0) {
                        tf = false;
                        break;
                    }

                }
                if(tf)result++;
            }
        }

        Console.WriteLine(result);
    }
}