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.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;

class Procon {
    static void Main (string[] agrs) {
        long A = Long();
        long B = Long();

        long tmp = gcd(A, B);

        int sqrt = (int)Math.Floor(Math.Sqrt((double)tmp));

        int ret = 1;
        for (int i = 2; i <= sqrt; i++) {
            if ((tmp % i) == 0){
                ret ++;
                tmp /= i;
                while ((tmp % i) == 0){
                    tmp /= i;
                }
            }
        }

        if (tmp != 1) {
            ret ++;
        }

        Console.WriteLine(ret);
    }

    static string String () => Scanner.nextString ();
    static int Int () => int.Parse (Scanner.nextString ());
    static long Long () => long.Parse (Scanner.nextString ());
    static double Double () => double.Parse (Scanner.nextString ());
    static char[] Chars () => String ().ToCharArray ();
    static string[] Strings () => Console.ReadLine ().Split (' ');
    static int[] Ints () => Strings ().Select (v => int.Parse (v)).ToArray ();
    static long[] Longs () => Strings ().Select (v => long.Parse (v)).ToArray ();
    static double[] Doubles () => Strings ().Select (v => double.Parse (v)).ToArray ();
    const int M = 1000000007;

    static long gcd(long a, long b)
    {
        long tmp;
        if (b > a)
        {
            tmp = a;
            a = b;
            b = tmp;
        }

        if (b == 0)
        {
            return a;
        }

        return gcd(b, a % b);
    }
}

class PriorityQueue<T> where T : IComparable<T> {
    public T[] heap;
    public int size;
    public int sign;
    public PriorityQueue (int N, bool descend = false) {
        heap = new T[N];
        sign = 1;
        if (descend) sign = -1;
    }
    public int Compare (T x, T y) {
        return x.CompareTo (y) * sign;
    }
    public void Push (T x) {
        int i = size++;
        while (i > 0) {
            int p = (i - 1) / 2;
            if (Compare (x, heap[p]) >= 0) {
                break;
            }
            heap[i] = heap[p];
            i = p;
        }
        heap[i] = x;
    }
    public T Pop () {
        T ret = heap[0];
        T x = heap[--size];
        int i = 0;
        while (i * 2 + 1 < size) {
            int a = i * 2 + 1;
            int b = i * 2 + 2;
            if (b < size && Compare (heap[a], heap[b]) > 0) {
                a = b;
            }
            if (Compare (heap[a], x) >= 0) {
                break;
            }
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        return ret;
    }
    public int Count () {
        return size;
    }
}

class Scanner {
    static string[] s = new string[0];
    static int i = 0;
    static int max_i = 0;
    static public string nextString () {
        if (i >= s.Length) {
            s = Console.ReadLine ().Split (' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0) {
                return "";
            }
            return s[i++];
        }
        return s[i++];
    }
}