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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;
	
	class Student
	{
		public int Index{get;set;}
		public int Count{get;set;}
	}
	public static void Main(string[] args)
	{
		string[] strin = Input();
		long a = strin[0].ToLong();
		long b = strin[1].ToLong();
		long gcd = GCD(a,b);
		
		List<long> cds = new List<long>();
		for(long i = 1; i <= gcd; i++)
		{
			if(a % i + b % i != 0) continue;
			//Console.WriteLine(i);
				cds.Add(i);
		}
		
		//List<int> cds2 = new List<int>();
		int[] ttt = new int[cds.Count];
		
		for(int i = 0; i < cds.Count; i++)
		{
			if(cds[i]==1 || ttt[i]==1)continue;
			for(int j =i ; j < cds.Count; j++)
			{
				if(cds[j] != cds[i] && cds[j] % cds[i]==0)
				ttt[j]=1;
			}
		}/*
		for(int i = 0; i < cds.Count; i++)
		{
			if(ttt[i]==1)continue;
			//Console.Write(cds[i] + " ");
		
		}*/
		Console.WriteLine(cds.Count);
	}
	private static void Divisors(long n )
	{
		
		long k = (long)(n/2)+1;
		for(long i = 1; i <= k; i++)
		{
			if(n % i == 0)
			{
			}
		}
	}
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(' '); }
	public static int Clamp(int val, int max, int min = 0) { return Math.Min(max, Math.Max(min, val)); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str)
	{
		int[] r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt();
		return r;
	 }
	
}