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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn vs(a: &mut Vec<Vec<usize>>, n: usize, p1: usize, p2: usize, done: &mut Vec<bool>) -> bool {
    if done[p2 - 1] {
        a[p1 - 1].push(p2);
        done[p1 - 1] = true;
        return false;
    } else if let Some(p3) = a[p2 - 1].pop() {
        if p1 != p3 {
            done[p1 - 1] = true;
            a[p1 - 1].push(p2);
            return vs(a, n, p2, p3, done);
        }
        done[p1 - 1] = true;
        done[p2 - 1] = true;
        return true;
    }
    false
}

fn day(a: &mut Vec<Vec<usize>>, n: usize) -> u32 {
    let mut done: Vec<bool> = vec![false; n];
    let mut cnt: u32 = 0;
    for p1 in 1..(n + 1) {
        if done[p1 - 1] {
            continue;
        } else if let Some(p2) = a[p1 - 1].pop() {
            if vs(a, n, p1, p2, &mut done) {
                cnt += 1;
            }
        }
    }
    cnt
}

fn all(a: &mut Vec<Vec<usize>>, n: usize) -> i32 {
    let mut vs_cnt: u32 = 0;
    let mut day_cnt: i32 = 0;

    while vs_cnt < ((n * (n - 1)) / 2) as u32 {
        let tmp = day(a, n);
        if tmp == 0 {
            day_cnt = -1;
            break;
        } else {
            vs_cnt += tmp;
        }
        day_cnt += 1;
    }

    return day_cnt;
}

fn gcd(x: u64, y: u64) -> u64 {
    if x > y {
        gcd_sub(x, y)
    } else {
        gcd_sub(y, x)
    }
}

fn gcd_sub(x: u64, y: u64) -> u64 {
    let r = x % y;
    if r == 0 {
        y
    } else {
        gcd_sub(y, r)
    }
}

fn main() {
    let ab: Vec<u64> = read_vec();
    let a: u64 = ab[0];
    let b: u64 = ab[1];
    let mut g = gcd(a, b);
    let max = ((g as f64).sqrt() as u64) + 10;
    let mut ans: u64 = 1;
    for i in 2..max {
        if g % i == 0 {
            ans += 1;
        }
        while g % i == 0 {
            g /= i;
        }
        if g == 1 {
            break;
        }
    }
    if (g > 1) {
        ans += 1;
    }
    println!("{}", ans);
}