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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
#include <vector>

using namespace std;

typedef long long ll;

template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

ll calc_lcd(ll x, ll y) {
    if (x == 0) {
        return y;
    }
    return calc_lcd(y % x, x);
}

// excluding 1
vector<ll> calc_divs(const ll x) {
    vector<ll> res;
    for (ll i = 1; i * i <= x; i++) {
        if (x % i == 0) {
            res.push_back(i);
            if (i * i != x) {
                res.push_back(x / i);
            }
        }
    }

    sort(res.begin(), res.end());
    return res;
}

int main(void) {
    ll A, B;
    cin >> A >> B;

    ll lcd;
    if (A < B) {
        lcd = calc_lcd(A, B);
    } else {
        lcd = calc_lcd(B, A);
    }

    // cout << "lcd: " << lcd << endl;

    vector<ll> divs = calc_divs(lcd);
    // for (int i = 0; i < (int) divs.size(); i++) {
    //     cout << divs[i] << " ";
    // }
    // cout << endl;

    int count = 1; // for 1
    vector<bool> flag((int) divs.size(), true);
    for (int i = 1; i < (int) flag.size(); i++) {
        if (flag[i]) {
            count++;
        }
        for (int j = i + 1; j < (int) flag.size(); j++) {
            if (divs[j] % divs[i] == 0) {
                flag[j] = false;
            }
        }
    }

    cout << count << endl;

    return 0;
}