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)

var GET = (function () {function f(s) {return new g(s);}function g(s) {this._s = s.trim().split("\n");}g.prototype.getValue = function (n) {return this._s[n];};g.prototype.getArray = function (n) {return this.stoa(this._s[n]);};g.prototype.slice = function (s, limit) {return this._s.slice(s, +limit + s || undefined).map(v => this.stox(v));};g.prototype.sliceArray = function (s, limit) {return this._s.slice(s, +limit + s || undefined).map(v => this.stoa(v));};g.prototype.stoa = function (s) {return s.split(" ").map(v => this.stox(v));};g.prototype.stox = function (v) {var i = +v;return (i === i) ? i : v;};return f;})();
var o = GET(require("fs").readFileSync("/dev/stdin", "utf8"));

console.log(main());
function main(){
    var l1 = o.getArray(0);
    var A = l1[0];
    var B = l1[1];

    var x, y;
    if (A >= B) {
        x = A;
        y = B;
    } else {
        x = B;
        y = A;
    }

    var r = x % y;
    while(r!=0){
        x = y;
        y = r;
        r = x % y;
    }

    var max = y;

    var divisors = makeDivisors(max);

    return divisors.length;
}


function makeDivisors(num) {
    var divisors = [1];

    var nums = Array.from((new Array(Math.floor(Math.pow(num, 0.5)) + 1)).keys());

    for (var i = 0; nums.length > i; i++) {
        var n = i + 1;
        if (num / n === 0) {
            if (isPrime(n)) divisors.push(n);
        }

        if (n !== num) {
            if (isPrime(n)) divisors.push(Math.floor(num/n) );
        }
    }

    return divisors;
}

function isPrime(num) {
    for(var i = 2; i < num; i++)
        if(num % i === 0) return false;
    return num > 1;
}