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";
    
const divisor = num => {
    let results = [];
    
    for(let i=1; i<=num; i++) {
        if( (num % i === 0) ) {
            results.push(i);
        }
    }
    
    return results;
}

const getGcd = (a, b) => {
  return a ? getGcd(b % a, a) : b;
}

const getPrimeFactors = n => {
    let result = [1];

    if (n === 1) {
        return [1];
    }

    let init = 2;

    while ( n !== 1 ) {
        
        let i = init;
        
        while (i < Number.MAX_SAFE_INTEGER) {
            if (n % i === 0) {
                result.push(i)
                n /= i;
                break;
            }
            i++;
        }
        
        init = i;
    }
    
    return result;
}

const main = arg => {
    arg = arg.trim().split("\n");
    const A = parseInt(arg[0].split(" ")[0]);
    const B = parseInt(arg[0].split(" ")[1]);
    
    // 最大公約数を見つける
    const gcd = getGcd(A, B);
    const primeFactors = [...new Set(getPrimeFactors(gcd))];
    
    let answer = primeFactors.length;
    
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));