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)

use std::cmp::min;
use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

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

#[allow(dead_code)]
fn main() {
    //let a = u32::max_value();
    //println!("{}", a + a);

    let a = read::<usize>();
    let b = read::<usize>();
    let mut g = gcd(a, b);
    let end = (g as f64).sqrt().ceil() as usize;

    let mut ans: usize = 0;
    for k in 2..end + 1 {
        let mut c = 0;
        while g % k == 0 {
            c += 1;
            g /= k
        }
        if c > 0 {
            ans += 1
        }
    }

    if g != 1 { // g == old g
        ans += 1;
    }
    println!("{}", ans + 1)
}