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)

macro_rules! input {
    ( $( $var:ident : $t:tt ),* ) => {
        use std::io::{stdin, Read};
        let mut bytes = stdin().bytes();
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        $(let $var = read_value!(next, $t);)*
    };

    ( $( $var:ident : $t:tt ),+ ,) => {
        input!{ $($var : $t),* }
    };
}

macro_rules! read_value {
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

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

fn main() {
    input! {
        a: usize,
        b: usize
    };

    let mut a = a;
    let mut b = b;
    let max = 10_usize.pow(6);
    let mut primes = vec![true; max + 1];
    let mut ans = 1;
    (2..max+1).map(|x| {
        if primes[x] {
            if a % x == 0 && b % x == 0 {
                while a % x == 0 {
                    a /= x;
                }
                while b % x == 0 {
                    b /= x;
                }
                ans += 1;
            }
            (2..max/x+1).map(|y| {
                primes[x * y] = false;
            }).collect::<Vec<_>>();
        }
    }).collect::<Vec<_>>();
    if gcd(a, b) != 1 {
        ans += 1;
    }
    println!("{}", ans);
}