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::{self, BufRead, BufWriter, Write};
use std::ops::Div;

fn solve<R, W>(reader: R, mut writer: W)
where
    R: BufRead,
    W: Write,
{
    let mut lines = reader.lines();
    let a_line = lines.next().unwrap().unwrap();
    let mut splited = a_line.trim().split_whitespace();
    let a: i64 = splited.next().unwrap().parse().unwrap();
    let b: i64 = splited.next().unwrap().parse().unwrap();

    let g = gcd(a, b);
    let ans = fact(g) + 1;

    writeln!(&mut writer, "{}", ans).unwrap();
}

fn gcd(x: i64, y: i64) -> i64 {
    let mut x = x;
    let mut y = y;
    while y != 0 {
        let t = y;
        y = x % y;
        x = t;
    }
    x
}

fn fact(mut n: i64) -> i64 {
    let s = (n as f64).sqrt() as usize;
    let mut result: i64 = 0;

    for i in 2..s + 1 {
        if n % i as i64 == 0 {
            loop {
                n = n.div(i as i64);
                if n % i as i64 != 0 {
                    break
                }
            };
            result += 1;
        }
    }

    if n > s as i64 {
        result += 1;
    }

    result
}

fn main() {
    let stdio = io::stdin();
    let input = stdio.lock();

    let stdout = io::stdout();
    let output = BufWriter::new(stdout.lock());

    solve(input, output);
}

#[cfg(test)]
mod tests {
    use super::*;

    const TESTS: &'static [(&'static [u8], &'static [u8])] = &[
        (
            br"12 18", br"3
",
        ),
        (
            br"420 660", br"4
",
        ),
        (
            br"1 2019", br"1
",
        ),
    ];

    #[test]
    fn test_d() {
        for &(input, expected) in TESTS {
            let mut output = Vec::new();
            solve(input, &mut output);
            let expected_str = String::from_utf8(expected.to_vec()).unwrap();
            let output_str = String::from_utf8(output).unwrap();
            assert_eq!(expected_str, output_str);
        }
    }
}