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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn divisors(n: usize) -> Vec<usize> {
    let mut d = vec![];
    for i in 1.. {
        if i * i > n {
            break;
        }
        if n % i == 0 {
            d.push(i);
            if i != n / i {
                d.push(n / i);
            }
        }
    }
    // d.sort();
    d
}

fn main() {
    input! {
        n: usize,
        m: usize,
    };

    let d = divisors(m);
    let mut ans = 1;
    for &d_i in d.iter() {
        if n * d_i <= m {
            ans = std::cmp::max(ans, d_i);
        }
    }
    println!("{}", ans);
}