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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

// inputに入力データ全体が入る
function Main(input) {
	// 1行目がinput[0], 2行目がinput[1], …に入る
	var Input = input.split(" ")
    
    var a = Number(Input[0])
    var b = Number(Input[1])
    
    var ans =  gcd(a,b)
    var cnt = 0
  	
    for(var i=1; i<= Math.sqrt(ans); i++){
      if(primeNumber(i) && ans % i == 0 ){
      cnt ++
        if( primeNumber(ans/i) && ans % i == 0 ){
          cnt ++
        }
      }
    }
    
  console.log(cnt)
  
}

function gcd(m,n){
  if (n == 0) return m;
  return gcd(n, m % n);
}

function primeNumber(n) {
 if (n === 2) return true;
 for (var i = 2; i <= Math.sqrt(n); i++) {
   if (n % i === 0) return false;
 }
 return true;
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));