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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            long A = cin.ReadLong;
            long B = cin.ReadLong;


            var gcd = Gcd(A, B);
            var divisor = GetDivisor(gcd);

            List<long> ans = new List<long>();
            foreach (var a in divisor)
            {
                // 互いに素か
                var commonDiv = a;
                var isCoprime = true;
                foreach (var ansTmp in ans)
                {
                    if (!coprime(ansTmp, a))
                    {
                        isCoprime = false;
                    }
                }
                if (isCoprime)
                    ans.Add(a);
            }
            WriteLine(ans.Count);

        }

        static long GcdArray(long[] array)
        {
            var ans = array[0];
            for(var i=1; i<array.Length; i++)
            {
                ans = Gcd(ans, array[i]);
            }
            return ans;
        }

        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];
        }

        static List<long> GetDivisor(long n)
        {
            List<long> divisor = new List<long>();
            for (var i=1; i*i<=n; i++)
            {
                if (n % i == 0)
                {
                    divisor.Add(i);
                    if (i != n / i)
                        divisor.Add(n / i);
                }
            }
            divisor.Sort();
            return divisor;

        }

        // 互いに素
        static bool coprime(long a, long b)
        {
            return (Gcd(a, b) == 1);
        }

        static long Lcm(long a, long b)
        {
            return a / Gcd(a, b) * b;
        }

        static bool ChMin<Type>(ref Type a, Type b)
            where Type : IComparable
        {   
            if(a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        static bool ChMax<Type>(ref Type a, Type b)
            where Type : IComparable
        {
            if (a.CompareTo(b) < 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }

    // From http://visualstudiomagazine.com/articles/2012/11/01/priority-queues-with-c.aspx
    public class PriorityQueue<T> where T : IComparable<T>
    {
        private List<T> data;

        public PriorityQueue()
        {
            this.data = new List<T>();
        }

        public void Enqueue(T item)
        {
            data.Add(item);
            int ci = data.Count - 1; // child index; start at end
            while (ci > 0)
            {
                int pi = (ci - 1) / 2; // parent index
                if (data[ci].CompareTo(data[pi]) >= 0)
                    break; // child item is larger than (or equal) parent so we're done
                T tmp = data[ci];
                data[ci] = data[pi];
                data[pi] = tmp;
                ci = pi;
            }
        }

        public T Dequeue()
        {
            // assumes pq is not empty; up to calling code
            int li = data.Count - 1; // last index (before removal)
            T frontItem = data[0];   // fetch the front
            data[0] = data[li];
            data.RemoveAt(li);

            --li; // last index (after removal)
            int pi = 0; // parent index. start at front of pq
            while (true)
            {
                int ci = pi * 2 + 1; // left child index of parent
                if (ci > li)
                    break;  // no children so done
                int rc = ci + 1;     // right child
                if (rc <= li && data[rc].CompareTo(data[ci]) < 0) // if there is a rc (ci + 1), and it is smaller than left child, use the rc instead
                    ci = rc;
                if (data[pi].CompareTo(data[ci]) <= 0)
                    break; // parent is smaller than (or equal to) smallest child so done
                T tmp = data[pi];
                data[pi] = data[ci];
                data[ci] = tmp; // swap parent and child
                pi = ci;
            }
            return frontItem;
        }

        public T Peek()
        {
            T frontItem = data[0];
            return frontItem;
        }

        public int Count()
        {
            return data.Count;
        }

        public override string ToString()
        {
            string s = "";
            for (int i = 0; i < data.Count; ++i)
                s += data[i].ToString() + " ";
            s += "count = " + data.Count;
            return s;
        }

        public bool IsConsistent()
        {
            // is the heap property true for all data?
            if (data.Count == 0)
                return true;
            int li = data.Count - 1; // last index
            for (int pi = 0; pi < data.Count; ++pi)
            { // each parent index
                int lci = 2 * pi + 1; // left child index
                int rci = 2 * pi + 2; // right child index

                if (lci <= li && data[pi].CompareTo(data[lci]) > 0)
                    return false; // if lc exists and it's greater than parent then bad.
                if (rci <= li && data[pi].CompareTo(data[rci]) > 0)
                    return false; // check the right child too.
            }
            return true; // passed all checks
        }
        // IsConsistent
    }
}