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::stdin;
use std::iter::Iterator;
use std::collections::VecDeque;
use std::collections::HashMap;

fn solve(cin: &mut ConsoleInputWrapper) {
    let a: i64 = cin.input().parse().unwrap();
    let b: i64 = cin.input().parse().unwrap();
    let gcd = gcd(a, b);
    let primes = factorization(gcd);
    println!("{}", primes.len() + 1);
    ()
}

//Other Functions Here

fn main() {
    let mut cin = ConsoleInputWrapper::new();
    solve(&mut cin);
}

fn factorization(value: i64) -> HashMap<i64, usize> {
    let sqrt = f64::sqrt(value.clone() as f64);
    let mut value = value;
    let mut map = HashMap::new();
    let mut p = 2;
    while p.clone() as f64 <= sqrt {
        let mut count = 0;
        while (value % p.clone()) == 0 {
            count += 1;
            value /= p.clone();
        }
        if count > 0 {
            map.insert(p.clone(), count);
        }
        p += 1;
    }
    if value != 1 {
        map.insert(value, 1);
    }
    map
}

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        a
    } else {
        gcd(b.clone(), a % b)
    }
}

fn min(a: i32, b: i32) -> i32 {
    if a < b { a } else { b }
}

fn max(a: i32, b: i32) -> i32 {
    if a > b { a } else { b }
}

struct ConsoleInputWrapper {
    queue: VecDeque<String>
}

impl ConsoleInputWrapper {
    fn new() -> ConsoleInputWrapper {
        ConsoleInputWrapper {
            queue: VecDeque::new()
        }
    }
    fn input(&mut self) -> String {
        if self.queue.len() <= 0 {
            let mut s = String::new();
            stdin().read_line(&mut s).unwrap();
            let list: Vec<&str> = s.split_whitespace().collect();
            for string in list {
                self.queue.push_back(String::from(string));
            }
        }
        self.queue.pop_front().unwrap()
    }
}