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)

#![allow(dead_code)]
#![allow(unused_must_use)]

fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(&src);

    let mut a : usize = sc.read();
    let mut b : usize = sc.read();

    let mut ans = 0;
    let mut not_prime = vec![false; 1__000_001];
    for i in 2..1_000_001 {
        if not_prime[i] { continue }
        let mut n = i;
        while n <= 1_000_000 {
            not_prime[n] = true;
            n += i;
        }
        if a % i == 0 && b % i == 0 {
            ans += 1;
        }
        while a % i == 0 {
            a /= i;
        }
        while b % i == 0 {
            b /= i;
        }
    }

    if a == b && a != 1 {
        ans += 1;
    }

    format!("{}", ans + 1)
}

#[test]
fn test() {
    assert_eq!(solve(r"12 18"),r"3");
    assert_eq!(solve(r"420 660"),r"4");
    assert_eq!(solve(r"1 2019"),r"1");
    assert_eq!(solve(r"2000000014 2000000014"), r"3");
}

fn main() {
    let mut buf = String::new();
    use std::io::Read;
    std::io::stdin().read_to_string(&mut buf);
    use std::io::Write;
    std::io::stdout().write_all(solve(&buf).as_bytes());
}

struct Scanner<I>{
    src: I
}

impl<'a> Scanner<std::str::SplitWhitespace<'a>> {
    fn from_str(src: &'a str) -> Self {
        Scanner { src: src.split_whitespace() }
    }
}

impl<'a, I> Scanner<I> where I: std::iter::Iterator<Item = &'a str>{
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.src.next().unwrap().parse().ok().expect("Parse error")
    }
    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    fn chars(&mut self) -> Vec<char> {
        self.src.next().unwrap().chars().collect()
    }
}