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: Wrong Answer)

fn main() {
    let vs = read_vec::<usize>();
    println!("{:?}", solve(vs[0], vs[1]));
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn solve(a: usize, b: usize) -> usize {
    let patterns = prime_patterns(gcd(a, b));
    patterns.len() + 1
}

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

fn is_prime(n: usize) -> bool {
    for i in 2..integer_sqrt(n) + 1 {
        if n % i == 0 {
            return false;
        }
    }
    true
}

fn prime_patterns(mut n: usize) -> Vec<usize> {
    let mut pattenrs = Vec::new();
    for i in 2..integer_sqrt(n) + 1 {
        if (is_prime(i)) && (n % i == 0) {
            pattenrs.push(i);
            n = n / i;
        }
    }
    pattenrs
}

fn integer_sqrt(n: usize) -> usize {
    let f = n as f64;
    f.sqrt().floor() as usize
}