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)

"use strict"

function sieveOfEratosthenes(n) {

 var primes = [];
 for (let i = 0; i <= n; i++) {
   primes[i] = true;
 }

 primes[0] = false;
 primes[1] = false;

 for (let i = 2; i <= Math.sqrt(n); i++) {
   for (let j = 2; j * i <= n; j++) {
     primes[i * j] = false;
   }
 }

 var result = [];

 for (let i = 0; i < primes.length; i++) {
   if (primes[i]) result.push(i);
 }

 return result;
}

const arg_str = require('fs').readFileSync('/dev/stdin', 'UTF-8')
const args_lines = arg_str.split(' ')
const A = parseInt(args_lines[0])
const B = parseInt(args_lines[1])

const X = Math.sqrt(A > B ? A : B)
const Y = sieveOfEratosthenes(Math.ceil(X))

Y.push(1)

const Z = Y.filter(x=>(A % x == 0 && B % x == 0))

if (Z.length == 1 && A == B && A > 1) Z.push(A)

console.log(Z.length)