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::cmp::max;
use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let n: u64 = read();
    let m: u64 = read();

    let mut ans = 0;

    for d in (1..m.isqrt() + 1).rev() {
        if m % d == 0 {
            if d >= n {
                ans = max(ans, m / d);
            }
            if m / d >= n {
                ans = max(ans, d);
            }
        }
    }

    println!("{}", ans);
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

// https://en.wikipedia.org/wiki/integer_square_root
trait IntegerSqrt {
    fn isqrt(&self) -> Self;
}

impl IntegerSqrt for u64 {
    fn isqrt(&self) -> Self {
        if *self < 2 {
            *self
        } else {
            let s = (*self >> 2).isqrt() << 1;
            let l = s + 1;
            if l * l > *self {
                s
            } else {
                l
            }
        }
    }
}