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::io;
use std::str::FromStr;


fn main() {
    let xs: Vec<i64> = reads();
    let x = xs[0];
    let y = xs[1];

    let g = gcd(x, y);
    let ans = cntprime(g);

    println!("{}", ans + 1);
}

#[allow(dead_code)]
fn getline() -> String {
    let mut ln = String::new();
    io::stdin().read_line(&mut ln).ok();
    ln.trim().to_string()
}

#[allow(dead_code)]
fn read<T>() -> T where T : FromStr {
    let mut ln = String::new();
    io::stdin().read_line(&mut ln).ok();
    ln.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn reads<T>() -> Vec<T> where T : FromStr {
    let mut ln = String::new();
    io::stdin().read_line(&mut ln).ok();
    ln.trim().split_whitespace().map(|x| x.parse().ok().unwrap()).collect()
}

#[allow(dead_code)]
fn printv<T>(xs: &[T]) where T : std::fmt::Display {
    xs.iter().fold("", |s, x| {
        print!("{}{}", s, x);
        " "
    });
    println!();
}

fn gcd(x: i64, y: i64) -> i64 {
    if y == 0 { return x; }
    gcd(y, x % y)
}

fn cntprime(mut x: i64) -> i64 {
    let ub = x;
    let mut res = 0;
    for i in 2..x+1 {
        if i * i > ub { break; }
        if x % i == 0 {
            res += 1;
            while x % i == 0 {
                x /= i;
            }
        }
    }
    if x > 1 { res += 1; }

    res
}