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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::collections::BTreeSet;

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

    let set = {
        let mut set = BTreeSet::new();
        for &(p,_) in &factor(a) {
            set.insert(p);
        }
        set
    };

    println!("{}",factor(b).iter().filter(|(p,_)| set.contains(&p)).count()+1)
}

pub fn factor(n: usize) -> Vec<(usize, usize)> {
    let mut n = n;
    let mut ret = vec![];
    let ps = primes((n as f64).sqrt() as usize + 2);
    for p in ps {
        let mut cnt = 0;
        while n % p == 0 {
            n /= p;
            cnt += 1;
        }
        if cnt > 0 {
            ret.push((p, cnt));
        }
    }
    if n > 1 {
        ret.push((n, 1));
    }
    ret
}

pub fn primes(n: usize) -> Vec<usize> {
    let mut tbl = vec![true; n];
    let mut ps = vec![];
    tbl[0] = false;
    tbl[1] = false;
    for i in 2..n {
        if tbl[i] {
            ps.push(i);
            let mut j = i + i;
            while j < n {
                tbl[j] = false;
                j += i;
            }
        }
    }
    ps
}