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)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}
use std::collections::HashSet;

fn divisors(n: i64) -> HashSet<i64> {
    let mut ds = vec![];
    let mut d = 1;
    while d * d <= n {
        if n % d == 0 {
            ds.push(d);
            ds.push(n / d);
        }
        d += 1;
    }
    let uniq: HashSet<i64> = ds.into_iter().collect();
    uniq
}

fn main() {
    let n: i64 = read();
    let m: i64 = read();

    let d = divisors(m);
    let mut ans = 0;

    for i in d {
        if (m / i) >= n {
            if i > ans {
                ans = i;
            }
        }
    }
    println!("{}", ans);
}