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 AtCoderBeginnerContest142.Questions;
using AtCoderBeginnerContest142.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoderBeginnerContest142.Questions
{
    public class QuestionD : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var ab = inputStream.ReadLongArray();
            var a = ab[0];
            var b = ab[1];

            var divisorsA = GetDivisors(a);
            var divisorsB = GetDivisors(b);
            var commonDivisors = GetCommonDivisors(divisorsA, divisorsB);

            yield return commonDivisors.Count;
        }

        private HashSet<long> GetDivisors(long n)
        {
            var sqrtN = (int)Math.Sqrt(n);
            var divisors = new HashSet<long>();
            divisors.Add(1);

            for (int i = 2; i <= sqrtN; i++)
            {
                while (n % i == 0)
                {
                    if (!divisors.Contains(i))
                    {
                        divisors.Add(i);
                    }
                    n /= i;
                }
            }

            if (n != 1)
            {
                divisors.Add(n);
            }

            return divisors;
        }

        private HashSet<long> GetCommonDivisors(HashSet<long> divisorsA, HashSet<long> divisorsB)
        {
            divisorsA.IntersectWith(divisorsB);
            return divisorsA;
        }
    }
}


namespace AtCoderBeginnerContest142
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtCoderBeginnerContest142.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace AtCoderBeginnerContest142.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion