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: Time Limit Exceeded)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::io::Read;
use std::io::{stdout, BufWriter, Write};

use std::collections::HashSet;

fn get_gcm(a: usize, b: usize) -> (usize, HashSet<usize>) {
    let mut a = a;
    let mut b = b;
    if (b > a) {
        let mut c = a;
        a = b;
        b = c;
    }
    
    let mut gcm = 1;
    
    //let mut vec = vec![1];
    
    let mut set = HashSet::new();
    
    set.insert(1);
    
    for i in 2..a+1 {
        while (a % i == 0 && b % i == 0) {
            a /= i;
            b /= i;
            
            gcm *= i;
            
            set.insert(i);
        }
    }
    
    (gcm, set)
}

fn main() {
    let mut buf = String::new();
    
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
 
    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();
 
    // 読み込んだStringを空白で分解する
    let mut iter = buf.split_whitespace();
 
    
    let a: usize = iter.next().unwrap().parse().unwrap();
    let b: usize = iter.next().unwrap().parse().unwrap();
    
    let (gcm, v) = get_gcm(a, b);
    
    //println!("{:?}",gcm);
    //println!("{:?}",v);
    
    println!("{}", v.len());
    
}