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::io;
use std::cmp;
fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N: i32 = iter.next().unwrap().parse().unwrap();
    let M: i32 = iter.next().unwrap().parse().unwrap();
    let mut max: i32 = 0;
    for d in divisor(M) {
        if M / d >= N {
            max = cmp::max(max, d);
        }
    }
    println!("{}", max);
}
fn divisor(n: i32) -> Vec<i32> {
    let mut res: Vec<i32> = Vec::new();
    let sqrtN: i32 = ((n as f64).sqrt() as i32) + 2;    
    for i in 1..sqrtN {
        if n % i == 0 {
            res.push(i);
            if n / i != i {
                res.push(n / i);
            }
        }
    }
    return res;
}