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 std::collections::HashMap;

#[fastout]
fn main() {
  input! {
    n: usize,
    m: usize,
  }
  
  if m % n == 0 {
    println!("{}", m / n);
    return
  }
  
  let mut map: HashMap<usize, bool> = HashMap::new();
  let mut i = 2;
  let mut v = m;
  while i * i <= m && 0 < v {
    if v % i == 0 {
      map.insert(i, true);
      v /= i;
    } else {
      i += 1;
    }
  }

  if map.keys().len() == 0 {
    println!("1");
    return
  }

  let mut v = m / n;
  while m % v != 0 || (m / v) < n {
    v -= 1;
  }
  println!("{}", v);
}