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,
  }
  
  let mut result = 1;
  let mut v = 1;
  while v * v <= m {
    if m % v == 0 {
      let b = m / v;
      if  v * n <= m {
        result = std::cmp::max(result, v);
      }
      if b * n <= m {
        result = std::cmp::max(result, b);
      }
    }
    v += 1;
  } 
  println!("{}", result);
}