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)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use nalgebra::max;

#[fastout]
fn main() {
    input! {
    n: usize,
    m: usize
    }
    let mut ans = 0;
    let d = divisor(m);
    for i in d {
        if m / i >= n {
            ans = i;
        }
    }
    println!("{}", ans);
}

fn divisor(m: usize) -> Vec<usize> {
    let mut l = Vec::new();
    for i in 1.. {
        if i * i > m {break}
        if m % i == 0 {
            l.push(i);
            l.push(m / i);
        }
    }
    l.sort();
    l.dedup();
    l
}