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.IO;
using System.Linq;
using System.Numerics;
using static Sample.Settings;
using static System.Math;

namespace Sample
{
    public sealed class Program : BaseProgram
    {
        public static void Main(string[] args)
        {
            using (var sc = new SetConsole()) { Solve(); }
        }
        public static void Solve()
        {
            var ab = GetArray<long>();
            var gcd = Gcd(ab[0], ab[1]);

            var result = new List<long>
            {
                gcd
            };
            for (int i = 1; i <= gcd / 2; i++)
            {
                if (gcd % i == 0)
                {
                    result.Add(i);
                }
            }
            var test = result.Where(r => IsPrime(r));
            Write(result.Where(r => IsPrime(r)).Count() + 1);

        }
        public static long Gcd(long a, long b)
        {
            if (a < b) { return Gcd(b, a); }
            var tmp = 0L;
            do
            {
                tmp = a % b;
                a = b;
                b = tmp;
            } while (tmp != 0);
            return a;
        }

        public static bool IsPrime(long num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

            double sqrtNum = Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {
                    // 素数ではない
                    return false;
                }
            }

            // 素数である
            return true;
        }
    }

    public class BaseProgram
    {
        protected static void Write<T>(T str) => Console.WriteLine(str);
        protected static string GetString() => Console.ReadLine();
        protected static T GetNumber<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var str = GetString();
            if (str == null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }

            var t = typeof(T);
            if ((t == typeof(byte)))
            {
                return (T)(object)str.ToByte();
            }
            else if (t == typeof(int))
            {
                return (T)(object)str.ToInt();
            }
            else if (t == typeof(long))
            {
                return (T)(object)str.ToLong();
            }
            else if (t == typeof(double))
            {
                return (T)(object)str.ToDouble();
            }
            throw new NotSupportedException();
        }
        protected static T[] GetArray<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var str = GetString();
            if (str == null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
            return str.ToArray<T>();
        }
        protected static TResult[] GetArray<TResult>(Func<string, TResult> selector)
        {
            var str = GetString();
            if (str == null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
            return (TResult[])(object)str.Split().Select(selector).ToArray();
        }
        protected static void Swap<T>(ref T item1, ref T item2)
        {
            var tmp = item1;
            item1 = item2;
            item2 = tmp;
        }
        protected class SetConsole : IDisposable
        {
            readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
            public SetConsole()
            {
                sw.AutoFlush = false;
                Console.SetOut(sw);
            }
            public void Dispose()
            {
                Console.Out.Flush();
                sw.AutoFlush = true;
                Console.SetOut(sw);
            }
        }
    }
    static class ExtentionsLibrary
    {
        public static List<T> CopyList<T>(this IReadOnlyList<T> list) => CopyArray(list.ToArray()).ToList();
        public static T[] CopyArray<T>(this T[] array)
        {
            var newArray = new T[array.Length];
            Array.Copy(array, newArray, array.Length);
            return newArray;
        }
        public static T[,] CopyArray<T>(this T[,] array)
        {
            var firstDimentionLength = array.GetLength(0);
            var secondDimentionLength = array.GetLength(1);
            var newDArray = new T[firstDimentionLength, secondDimentionLength];
            Array.Copy(array, newDArray, firstDimentionLength * secondDimentionLength);
            return newDArray;
        }
        public static T[] ToArray<T>(this string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            if (typeof(T) == typeof(string)) { return (T[])(object)str.Split(); }

            return str.ConvertEnumerator<T>().ToArray();
        }
        public static IEnumerable<T> ConvertEnumerator<T>(this string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var t = typeof(T);
            if (t == typeof(byte))
            {
                return (IEnumerable<T>)str.Split().Select(byte.Parse);
            }
            if (t == typeof(int))
            {
                return (IEnumerable<T>)str.Split().Select(int.Parse);
            }
            if (t == typeof(long))
            {
                return (IEnumerable<T>)str.Split().Select(long.Parse);
            }
            if (t == typeof(double))
            {
                return (IEnumerable<T>)str.Split().Select(double.Parse);
            }
            if (t == typeof(BigInteger))
            {
                return (IEnumerable<T>)str.Split().Select(BigInteger.Parse);
            }
            throw new NotSupportedException();
        }
        public static byte ToByte(this string str) => byte.Parse(str);
        public static byte ToByte(this char chr) => byte.Parse(chr.ToString());
        public static int ToInt(this string str) => int.Parse(str);
        public static int ToInt(this char chr) => int.Parse(chr.ToString());
        public static long ToLong(this string str) => long.Parse(str);
        public static double ToDouble(this string str) => double.Parse(str);
        public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
        public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
        public static string StringJoin(this object[] array, string separator) => string.Join(separator, array);
        public static string StringJoin<T>(this IEnumerable<T> collection, string separator) => string.Join(separator, collection.Select(c => c.ToString()));
    }
    public class PriorityQueue<T> : IEnumerable<T> where T : IComparable<T>
    {
        private readonly Priority priority;
        private List<T> heap = new List<T> { default(T) };

        private PriorityQueue() { }
        public PriorityQueue(Priority p)
        {
            priority = p;
        }
        public int Count() => heap.Count - 1;
        public T Peek()
        {
            if (Count() <= 0) { throw new Exception("要素が空です"); }
            return heap[1];
        }
        public T Dequeue()
        {
            if (Count() <= 0) { throw new Exception("要素が空です"); }

            var max = heap[1];
            heap[1] = heap[heap.Count - 1];
            heap.RemoveAt(heap.Count - 1);
            MaxHeapify(1);
            return max;
        }
        public void Enqueue(T key)
        {
            HeapIncreaseKey(key);
        }
        public void EnqueueRange(IEnumerable<T> keys)
        {
            foreach (var key in keys) { HeapIncreaseKey(key); }
        }
        public void Clear()
        {
            heap = new List<T>() { default(T) };
        }
        private void MaxHeapify(int i)
        {
            int largest;
            int l = Left(i);
            int r = Right(i);

            if (l <= heap.Count - 1 && Compare(heap[i], heap[l]) < 0)
            {
                largest = l;
            }
            else
            {
                largest = i;
            }
            if (r <= heap.Count - 1 && Compare(heap[r] ,heap[largest]) > 0)
            {
                largest = r;
            }

            if (largest != i)
            {
                var temp = heap[i];
                heap[i] = heap[largest];
                heap[largest] = temp;
                MaxHeapify(largest);
            }
        }
        private void HeapIncreaseKey(T key)
        {
            heap.Add(key);
            int lastIndex = heap.Count - 1;
            while (lastIndex > 1 && Compare(heap[Parent(lastIndex)], heap[lastIndex]) < 0)
            {
                var temp = heap[lastIndex];
                heap[lastIndex] = heap[Parent(lastIndex)];
                heap[Parent(lastIndex)] = temp;
                lastIndex = Parent(lastIndex);
            }
        }
        private static int Parent(int i) => i / 2;
        private static int Left(int i) => i * 2;
        private static int Right(int i) => i * 2 + 1;
        private int Compare(T x, T y) => priority == Priority.Larger ? x.CompareTo(y) : y.CompareTo(x);
        IEnumerator<T> IEnumerable<T>.GetEnumerator() => heap.Skip(1).GetEnumerator();
        public IEnumerator GetEnumerator()
        {
            return heap.Skip(1).GetEnumerator();
        }
    }
    public class Settings
    {
        public enum Priority : byte
        {
            Smaller = 0,
            Larger = 1
        }
    }
}