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.Generic;
using System.Linq;

namespace abc142_d
{
    class Program
    {
        static void Main(string[] args)
        {
            var AB = GetLongList();
            var a = GetDivisors(AB[0]);
            var b = GetDivisors(AB[1]);
            var c = a.Intersect(b).ToList();
            
            //Console.WriteLine(string.Join(" ", a));
            //Console.WriteLine(string.Join(" ", b));
            //Console.WriteLine(string.Join(" ", c));

            if (c.Count() == 1)
                Console.WriteLine(1);
            else if (c.Count() == 2) 
            {
                if (Coprime(c[0], c[1]))
                    Console.WriteLine(2);
                else
                    Console.WriteLine(1);
            }
            else
            {
                long? c2min = null;

                if (c.Where(x => x % 2 == 0).Any())
                    c2min = c.Where(x => x % 2 == 0).Min();

                // 偶数を削除
                c = c.Where(x => x % 2 != 0).ToList();

                // 最小の偶数を追加
                if (c2min != null) c.Add((long)c2min);

                for (int i = c.Count(); i >= 2; i--)
                {
                    var cc1 = EnumerateCombination(c.Count(), i);

                    var cc2 = EnumerateCombination(i, 2);

                    for (int j = 0; j < cc1.Count; j++)
                    {
                        //Console.WriteLine(string.Join(" ", cc1[j]));

                        int r = 0;
                        foreach (var cci in cc2)
                        {
                            var cc31 = c[cc1[j][cci[0]]];
                            var cc32 = c[cc1[j][cci[1]]];
                            //Console.Write(cc31 + " " + cc32 + " | ");

                            if (Coprime(cc31, cc32)) r++;
                            else
                            {
                                //Console.Write("NG ");
                                break;
                            }
                        }
                        //Console.WriteLine("");

                        if (r == cc2.Count())
                        {
                            Console.WriteLine(i);
                            return;
                        }

                    }

                }

                Console.WriteLine(1);

            }

        }

        /// <summary>
        /// 約数の列挙
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static List<long> GetDivisors(long n)
        {
            var divisors = new List<long>();
            for (int i = 1; i <= Math.Sqrt(n); i++)
            {
                if (n % i == 0)
                {
                    divisors.Add(i);
                    if (i != Math.Floor((decimal)n / i))
                        divisors.Add((long)Math.Floor((decimal)n / i));
                }
            }

            return divisors;

        }

        /// <summary>
        /// 互いに素
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static bool Coprime(long a, long b)
        {
            return Gcd(a, b) == 1;
        }

        /// <summary>
        /// 最大公約数：ユークリッドの互除法 
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static long Gcd(long a, long b)
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }

        /// <summary>
        /// 組み合わせ生成クラス　数字のみ高速
        /// </summary>
        /// <param name="n"></param>
        /// <param name="m"></param>
        /// <returns></returns>
        static List<int[]> EnumerateCombination(int n, int m)
        {
            var all = new List<List<int>>[n];
            for (int i = 0; i <= n - m; i++)
            {
                var list = new List<int>();
                list.Add(i);
                all[i] = new List<List<int>>();
                all[i].Add(list);
            }

            for (int i = 1; i < m; i++)
            {
                var next = new List<List<int>>[n];
                for (int j = i; j <= n - m + i; j++)
                {
                    next[j] = new List<List<int>>();
                    for (int k = i - 1; k < j; k++)
                    {
                        for (int l = 0;
                            all[k] != null && l < all[k].Count; l++)
                        {
                            var list = new List<int>();
                            list.AddRange(all[k][l]);
                            list.Add(j);
                            next[j].Add(list);
                        }
                    }
                }
                all = next;
            }

            var res = new List<int[]>();
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; all[i] != null && j < all[i].Count; j++)
                {
                    res.Add(all[i][j].ToArray());
                }
            }
            return res;
        }

        public static string GetStr() => Console.ReadLine();
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static decimal GetDecimal() => decimal.Parse(Console.ReadLine());

        public static List<string> GetStrList() => Console.ReadLine().Split(' ').ToList();
        public static List<int> GetIntList() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
        public static List<long> GetLongList() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
        public static List<double> GetDoubleList() => Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToList();
        public static List<decimal> GetDecimalList() => Console.ReadLine().Split(' ').Select(x => decimal.Parse(x)).ToList();


    }
}