Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Rust (1.15.1) (judge verdict: Accepted)


fn func(input_str: &str) {
    let mut iter = input_str.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let m: usize = iter.next().unwrap().parse().unwrap();
    if n == 1 {
        println!("{}", m);
        return;
    }
    let mut divisors = Vec::new();
    for c in 2..((m as f64).sqrt() as usize + 1) {
        if m % c == 0 {
            if n <= m / c {
                divisors.push(c);
            }
            if n <= c {
                divisors.push(m / c);
            }
        }
    }
    divisors.sort();
    if let Some(c) = divisors.last() {
        println!("{}", c);
    } else {
        println!("{}", 1);
    }
}

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    func(&buf[..]);
}