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;
using System.Collections.Generic;
using System.ComponentModel;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using static System.Console;
using static System.Math;
using static Utils;
class Program
{


    void Solve()
    {
        var A = io.Long;
        var B = io.Long;
        
        var ap = primeFactor(A);
        var bp = primeFactor(B);
        var factor = ap.Keys.Where(k => bp.ContainsKey(k));

        WriteLine(factor.Count() + 1);

    }
    Dictionary<long, int> primeFactor(long n)
    {
        var ret = new Dictionary<long, int>();
        for (var i = 2; i <= n; ++i)
        {
            if (!ret.ContainsKey(i)) ret[i] = 0;
            while (n % i == 0)
            {
                ++ret[i];
                n /= i;
            }
        }
        return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Program().Stream();
    private void Stream()
    {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //SetIn(exStdIn);
        Solve();
        io.Flush();
    }

}

class SimpleIO
{
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] { ' ', '"', ',' };
    StreamWriter sw = new StreamWriter(OpenStandardOutput())
    {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public SimpleIO()
    {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        SetOut(sw);
    }
    string Next()
    {
        if (_bufferCnt < _nextBuffer.Length) return _nextBuffer[_bufferCnt++];
        var st = ReadLine();
        while (st == string.Empty) st = ReadLine();
        _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() => Out.Flush();
}
static class Utils
{
    public static T id<T>(T x) => x;
    public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
    public static void FOR(int a, int b, int n, Action<int> f)
    {
        for (int i = a; i < b; i += n) f(i);
    }
    public static void REP(int a, Action<int> f) => FOR(0, a, f);
    public class IndexedItem<T>
    {
        public int Idx;
        public T Val;
        public IndexedItem(int idx, T val)
        {
            Idx = idx;
            Val = val;
        }
    }
    public static IEnumerable<IndexedItem<T>> Indexed<T>(this IEnumerable<T> xs) => xs.Select((x, i) => new IndexedItem<T>(i, x));
}