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: Time Limit Exceeded)

'use strict'
function main(inp) {
  inp = inp.trim().split(' ').map(n => Number(n));
  const gcd = (x, y) => y === 0 ? x : gcd(y, x%y)
  const G = gcd(...inp)

  let arr = [1]
  for (let i = 2; i <= G; i++) {
    if ((inp[0] % i === 0) && (inp[1] % i === 0)) {
      let isSO = true
      for (let j = 1; j < arr.length; j++) {
        if (gcd(arr[j], i) !== 1) {
          isSO = false
          break;
        }
      }
      if (isSO) arr.push(i)
    }
  }
  console.log(arr.length);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));