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: Wrong Answer)

// Try AtCoder
// author: Leonardone @ NEETSDKASU

fn main() {
	let mut stdin = String::new();
    std::io::Read::read_to_string(
    	&mut std::io::stdin(),
        &mut stdin).unwrap();
	let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
    	($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    let n = get!();
    let m = get!();
    
    let ai = m / n;
    let rem = m % n;
    
    if rem == 0 {
    	println!("{}", ai);
        return;
    }
    
    if n == 2 {
    	let ans = gcd(ai, ai + rem);
        println!("{}", ans);
        return;
    }
    
    let mut ans = 0;
    for i in 1..rem+1 {
    	let p = rem / i;
        let q = rem % i;
        let a1 = ai + p;
        let a2 = ai + p + q;
        let g = gcd(ai, a1);
        let g = gcd(g, a2);
        ans = std::cmp::max(ans, g);
    }
    
    println!("{}", ans);    
}

fn gcd(a: i64, b: i64) -> i64 {
	if a == 0 {
    	return b;
    }
    return gcd(b % a, a);
}