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;

class Program
{
    //static int[] dp;
    //static decimal[,,] dp;
    //static decimal N;
    static void Main(string[] args)
    {
        // 入力
        long[] input = Console.ReadLine().Split().Select(p => long.Parse(p)).ToArray();
        long A = input[0];
        long B = input[1];

        HashSet<long> ret = new HashSet<long>();

        long last = (long)Math.Ceiling(Math.Min(Math.Sqrt((double)A), Math.Sqrt((double)B)));
        for(int i=2; i <= last+1; i++)
        {
            // iで割り切れるだけ割る
            if(A%i == 0 && B%i == 0)
            {
                ret.Add(i);
            }
            if(A%i == 0)
            {
                while(A%i == 0)
                {
                    A /= i;
                }
            }
            if (B%i == 0)
            {
                while (B % i == 0)
                {
                    B /= i;
                }
            }
        }

        // 小さいほう(素数)が大きいほうを割り切れる場合
        if(A > 1 && A<B)
        {
            if(B%A==0)
            ret.Add(A);
        }
        else if(B > 1)
        {
            if (A % B == 0)
                ret.Add(B);
        }
        Console.WriteLine((ret.Count+1) + "");
    }
}