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(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn main() {
    let (a, b) = get!(usize, usize);
    let gcd = gcd(a, b);
    let v = make_divisors(gcd);
    // eprintln!("{:?}", v);
    let mut ans = 1;
    for i in 0..v.len() {
        if is_prime(v[i]) {
            ans += 1;
        }
    }
    println!("{}", ans);
}

fn gcd(a: usize, b: usize) -> usize {
    let mut a = a;
    let mut b = b;
    while b != 0 {
        let r = b;
        b = a % b;
        a = r;
    }
    a
}

fn make_divisors(n: usize) -> Vec<usize> {
    let mut v = Vec::new();
    for i in 1..n + 1 {
        if n < i * i {
            break;
        }
        if n % i == 0 {
            v.push(i);
            if n / i != i {
                v.push(n / i);
            }
        }
    }
    v
}
fn is_prime(n: usize) -> bool {
    if n <= 3 {
        if n == 0 || n == 1 {
            return false;
        } else {
            return true;
        }
    }
    if n % 2 == 0 {
        return false;
    }
    if n % 3 == 0 {
        return false;
    }
    if n % 6 != 1 && n % 6 != 5 {
        return false;
    }
    let mut i = 5;
    while i * i <= n {
        if n % i == 0 {
            return false;
        }
        if n % (i + 2) == 0 {
            return false;
        }
        i += 6;
    }
    true
}