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;
use std::collections::HashSet;
fn main() {
    input! {
        n: usize,
        m: usize
    };
    let bound = (m as f64).sqrt().floor() as usize;
    let mut divs = HashSet::new();
    for i in 1..bound+1 {
        if m % i == 0 {
            divs.insert(i);
            divs.insert(m/i);
        } else {}
    }
    let ans = divs.iter().map(|x| *x).filter(|x| m/x >= n).max().unwrap();
    println!("{}", ans);
}