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 read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("faild to read char") as char)
        .take_while(|c| !c.is_whitespace())
        .collect();
    token
        .parse()
        .ok()
        .expect("faild to parse token")
}

fn main(){
    let mut g = gcd(read(), read());
    let mut ret = 1;

    for i in 2..g {
        let mut n = 0;
        if g < i * i {
            break;
        }
        while g % i == 0 {
            g /= i;
            n += 1;
        }
        if n > 0 {
            ret += 1;
        }
    }

    if g > 1 {
        ret += 1;

    }
    println!("{}", ret);
}

fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        return a;
    }
    gcd(b, a % b)
}