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)

namespace AtCoder.ABC.D142
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Numerics;
    using System.IO;

    using AtCoder.ABC.IO;

    public class Quest
    {
        public object Solve(Parser parser)
        {
            long a = parser.Long();
            long b = parser.Long();

            if (a == 1 && b == 1)
            {
                return 1;
            }

            var factorsA = ComputePrimeFactors(a).Select(x => x.Key);
            var factorsB = ComputePrimeFactors(b).Select(x => x.Key);

            HashSet<long> set = new HashSet<long>();

            foreach (var item in factorsA.Intersect(factorsB))
            {
                set.Add(item);
            }

            return set.Count + 1;
        }

        private Dictionary<long, long> ComputePrimeFactors(long n)
        {
            var map = new Dictionary<long, long>();
            if (n == 1)
            {
                if (!map.ContainsKey(n)) map.Add(n, 0);
                map[n] = 1;
                return map;
            }
            for (long i = 2, _n = n; i * i <= _n; ++i)
            {
                while (n % i == 0)
                {
                    if (!map.ContainsKey(i)) map.Add(i, 0);
                    map[i] += 1;
                    n /= i;
                }
            }
            if (n != 1)
            {
                if (!map.ContainsKey(n)) map.Add(n, 0);
                map[n] = 1;
            }
            return map;
        }
    }

    static class Program
    {
        static void Main(string[] args)
        {
            var i = new Parser(Console.OpenStandardInput());
            var o = new Printer(Console.OpenStandardOutput());
            var got = new Quest().Solve(i);
            o.WriteLine(got);
            o.Flush();
        }
    }
}
namespace AtCoder.ABC.IO
{
    #region IO

    using System;
    using System.IO;
    using System.Text;
    using System.Linq;
    using System.Collections.Generic;
    using System.Globalization;

    public class Parser
    {
        public Parser(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        public IEnumerable<Parser> Take(int n)
        {
            return Enumerable.Range(1, n).Select(_ => this);
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    #endregion

}