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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.stream.LongStream;

class Solver {

    private final long A;
    private final long B;

    Solver(Scanner in) {
        A = in.nextLong();
        B = in.nextLong();
    }

    void solve() {
        System.out.println(factorize(gcd(A, B)).length);
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long[] factorize(long x) {
        LongStream.Builder builder = LongStream.builder();
        long i = 1;
        for (; i * i <= x; i++) {
            if (x % i == 0) {
                x /= i;
                builder.accept(i);
            }
        }
        if (x != 1) builder.accept(i);
        return builder.build().toArray();
    }
}

class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        new Solver(in).solve();

        in.close();
    }
}