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)

use std::cmp;

use num_integer::gcd;
use proconio::input;

#[proconio::fastout]
fn main() {
    input! {
        N: i128,
        M: i128
    }
    if N == 1 {
        println!("{}", M);
        return;
    }
    let mut max = 1;
    let mut x = 2;
    while x * x < M {
        if M % x == 0 {
            max = cmp::max(gcd(x, cmp::max(M - x * (N - 1), 1)), max);
            max = cmp::max(gcd(M / x, cmp::max(M - (M / x) * (N - 1), 1)), max);
        }
        x += 1;
    }
    println!("{}", max);
}