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 Rust (1.15.1) (judge verdict: Accepted)

fn gcd(a: i64,  b: i64) -> i64 {
    if a % b == 0 {
        return b
    } else {
        return gcd(b, a % b)
    }
}

#[test]
fn gcd_test() {
    assert_eq!(gcd(3, 5), 1);
    assert_eq!(gcd(8, 12), 4);
    assert_eq!(gcd(12, 12), 12);
}


fn main() {
    let mut k = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line);
        let s = line.split_whitespace().map(|a| a.parse().unwrap()).collect::<Vec<i64>>();
        gcd(s[0], s[1])
    };
    let mut count = 1;
    for i in 2i64..2000000 {
        if k % i == 0 {
            count += 1
        }
        while k % i == 0 {
            k /= i
        }
    }
    if k > 1 {
        count += 1
    }
    println!("{}", count);
}