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)

// ReSharper disable ArrangeTypeMemberModifiers
// ReSharper disable ConvertIfStatementToSwitchStatement
// ReSharper disable FunctionRecursiveOnAllPaths
// ReSharper disable InconsistentNaming
// ReSharper disable InlineOutVariableDeclaration
// ReSharper disable InvertIf
// ReSharper disable JoinDeclarationAndInitializer
// ReSharper disable MemberCanBeMadeStatic.Global
// ReSharper disable MemberCanBeMadeStatic.Local
// ReSharper disable NonReadonlyMemberInGetHashCode
// ReSharper disable PossibleNullReferenceException
// ReSharper disable RedundantUsingDirective
// ReSharper disable SuggestVarOrType_BuiltInTypes
// ReSharper disable SuggestVarOrType_Elsewhere
// ReSharper disable TailRecursiveCall
// ReSharper disable UnusedMember.Global
// ReSharper disable UnusedMember.Local
// ReSharper disable UseObjectOrCollectionInitializer

#if true && UTAKA_LOCAL
//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Text;

namespace UtakaApp
{
    public class Program
    {
        public const string SiteName = "AtCoder";
        public const string ContestName = "abc142";
        public const string ProblemName = "D";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var console = new MyConsole();
            new Program().Solve(System.Console.In, console);
            console.Flush();
#endif
        }

        public void Solve(TextReader textReader, IConsole console)
        {
            var cin = new ConsoleInput(textReader);

            long A = cin.ReadLong;
            long B = cin.ReadLong;

//            var aMap = FactorizeAsMap(A);
//            var bMap = FactorizeAsMap(B);
//            
//            var hashSet = new HashSet<long>();
//            
//            hashSet.UnionWith(aMap.Keys);
//            hashSet.IntersectWith(bMap.Keys);
//
//            var result = hashSet.Count + 1;

            var gcd = Gcd(A, B);

            var map = FactorizeAsMap(gcd);

            var count = map.Count + 1;
            console.WriteLine(count.ToString());
        }
        
        public static long Calc(long value)
        {
            long count = 0;
            
            long first = value;
            for (long i = 2; i * i < first; i++)
            {
                while (value % i == 0)
                {
                    value /= i;
                    count++;
                }
            }

            if (value > 1)
            {
                count++;
            }

            return count;
        }

        public void WriteEnumerable<T>(IEnumerable<T> A, IConsole console, string delimiter = " ")
        {
            var sb = new StringBuilder();
            foreach (T v in A)
            {
                sb.Append(v);
                sb.Append(delimiter);
            }

            if (sb.Length > 0)
            {
                sb.Length--;
            }

            console.WriteLine(sb.ToString());
        }
        
        public static long Gcd(long a, long b)
        {
            while (a != 0 && b != 0)
            {
                if (a > b)
                    a %= b;
                else
                    b %= a;
            }

            return a == 0 ? b : a;
        }
        
        
        public static ulong Gcd(ulong a, ulong b)
        {
            while (a != 0 && b != 0)
            {
                if (a > b)
                    a %= b;
                else
                    b %= a;
            }

            return a == 0 ? b : a;
        }
        
        public static ulong Lcm(ulong a, ulong b)
        {
            return a / Gcd(a, b) * b;
        }

        /// <summary>
        /// valueを素因数分解し、素因数を列挙します。
        /// </summary>
        /// <param name="value">素因数分解する値</param>
        /// <returns>素因数の集合</returns>
        public static IEnumerable<int> Factorize(int value)
        {
            int first = value;
            for (int i = 2; i * i < first; i++)
            {
                while (value % i == 0)
                {
                    value /= i;
                    yield return i;
                }
            }

            if (value > 1)
                yield return value;
        }

        /// <summary>
        /// valueを素因数分解し、素因数を列挙します。
        /// </summary>
        /// <param name="value">素因数分解する値</param>
        /// <returns>素因数の集合</returns>
        public static IEnumerable<long> Factorize(long value)
        {
            long first = value;
            for (long i = 2; i * i < first; i++)
            {
                while (value % i == 0)
                {
                    value /= i;
                    yield return i;
                }
            }

            if (value > 1)
                yield return value;
        }

        /// <summary>
        /// valueを素因数分解し、素因数とその個数の連想配列を返します。
        /// </summary>
        /// <param name="value">素因数分解する値</param>
        /// <returns>素因数の連想配列</returns>
        public static Dictionary<long, int> FactorizeAsMap(long value)
        {
            var dict = new Dictionary<long, int>();
            long first = value;
            for (int i = 2; i * i < first; i++)
            {
                if (value % i > 0) continue;
                int cnt = 0;
                while (value % i == 0)
                {
                    value /= i;
                    cnt++;
                }

                dict.Add(i, cnt);
            }

            if (value > 1) dict.Add(value, 1);
            return dict;
        }

        /// <summary>
        /// valueを素因数分解し、素因数とその個数の連想配列を返します。
        /// </summary>
        /// <param name="value">素因数分解する値</param>
        /// <returns>素因数の連想配列</returns>
        public static Dictionary<int, int> FactorizeAsMap(int value)
        {
            var dict = new Dictionary<int, int>();
            int first = value;
            for (int i = 2; i * i < first; i++)
            {
                if (value % i > 0) continue;
                int cnt = 0;
                while (value % i == 0)
                {
                    value /= i;
                    cnt++;
                }

                dict.Add(i, cnt);
            }

            if (value > 1) dict.Add(value, 1);
            return dict;
        }

        /// <summary>
        /// valueの約数の個数を求めます。
        /// </summary>
        /// <param name="value">約数の個数を求める数</param>
        /// <returns>valueの約数の個数</returns>
        public static long Divisors(long value)
        {
            var fact = FactorizeAsMap(value);
            return fact.Select(x => x.Value + 1L).Aggregate((m, x) => m * x);
        }
    }


    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private readonly char _separator = ' ';
        private readonly Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            _separator = separator;
            _stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0)
                {
                    return inputStream.Dequeue();
                }

                var tmp = _stream.ReadLine().Split(_separator);
                for (var i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => 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;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(string str);
        void WriteLine(string str);
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
        }

        public void Flush()
        {
            Console.Out.Flush();
        }

        public void Write(string str)
        {
            Console.Write(str);
        }

        public void WriteLine(string str)
        {
            Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private readonly StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string GetDirectoryPath()
        {
            var problemPart = string.IsNullOrEmpty(Program.ProblemName)
                ? ""
                : $"/{Program.ProblemName}";

            return
                $"{System.Environment.GetFolderPath(Environment.SpecialFolder.UserProfile)}/AlgorithmPrac/{Program.SiteName}/{Program.ContestName}{problemPart}";
        }

        private string GetInputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.in";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.out";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsole();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems(int targetTestCaseNumber = -1)
        {
            bool isSuccessAll = true;

            int testCaseNumber = 0;
            while (true)
            {
                testCaseNumber++;

                if (targetTestCaseNumber >= 0 && targetTestCaseNumber != testCaseNumber)
                {
                    continue;
                }

                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    Console.WriteLine("Success");
                }
                else
                {
                    isSuccessAll = false;
                    Console.WriteLine("Failure *****");
                }
            }

            if (isSuccessAll)
            {
                Console.WriteLine("!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}