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)

using System;
using System.Collections.Generic;

class Program{
  static void Main(){
    string[] input = Console.ReadLine().Split(' ');
    long A = long.Parse(input[0]);
    long B = long.Parse(input[1]);
    long G = Gcd(A, B);
    Console.WriteLine(HowManyFactors(G) + 1);
  }
  
  // 最大公約数
  static long Gcd(long a, long b){
    if (a < b)
      return Gcd(b, a);
    while (b != 0) {
      long tmp = a % b;
      a = b;
      b = tmp;
    }
    return a;
  }
  
  // 与えられた整数の素因数の個数を返す
  static int HowManyFactors(long N){
    // 素因数を格納しておくもの
    var flist = new List<long>();
    flist.Add(1);
    int i = 0;  // flist.Length - 1 と同じ
    
    long factor = 2;
    long tmp = N;
    
    while (factor * factor <= N){
      if (tmp % factor == 0){ //factorで割り切れるなら
        if (flist[i] != factor){// そのfactorが新出なら
          flist.Add(factor); // listに追加
          i++;
        }
        tmp = tmp / factor;
      }
      else
        factor++;
    }
    
    // 最大の素因数
    if (tmp != 1){
      flist.Add(factor);
      i++;
    }
    
    return i;
  }
}