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: Time Limit Exceeded)

fn main() {
    // input
    let one = read_vec::<u64>();
    // A
    let a = one[0];
    // B
    let b = one[1];

    let a_uniq = calc_uniq_so_koyakusus(a);
    let b_uniq = calc_uniq_so_koyakusus(b);

    let mut ans = 1 as u64;

    for a in a_uniq {
        if b_uniq.contains(&a) {
            ans += 1;
        }
    }

    println!("{}", ans);
}

fn calc_uniq_so_koyakusus(i: u64) -> Vec<u64> {
    let mut now = i;
    let mut ans = Vec::new();
    let mut koyakusu = 1;

    loop {
        koyakusu = calc_min_koyakusu(now, koyakusu);
        if koyakusu == 0 {
            break;
        } else {
            ans.push(koyakusu);
            // uniq
            while now % koyakusu == 0 {
                now = now / koyakusu;
            }
        }
    }

    return ans;
}

fn calc_min_koyakusu(i: u64, now: u64) -> u64 {
    // println!("{} {}", i, now);
    if i < now {
        return 0;
    }
    for n in now + 1..i / 2 {
        if i % n == 0 {
            return n;
        }
    }
    return i;
}

#[allow(dead_code)]
fn read_line<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read_line::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}