Problem:
Score : 800 points

Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.

Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

1 \leq N,K \leq 3 × 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

K N

Output

Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

Sample Input 1

3 2

Sample Output 1

2 1

There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).
The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

Sample Input 2

2 4

Sample Output 2

1 2 2 2

Sample Input 3

5 14

Sample Output 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn prev(a: &mut Vec<usize>, k: usize, n: usize) {
    if *a.last().unwrap() == 0 {
        a.pop();
    } else {
        *a.last_mut().unwrap() -= 1;
        while a.len() < n {
            a.push(k - 1);
        }
    }
}

fn main() {
    input!(k: usize, n: usize);
    let ans: Vec<usize> = {
        if k % 2 == 0 {
            std::iter::once(k / 2 - 1)
                .chain(std::iter::repeat(k - 1).take(n - 1))
                .collect()
        } else {
            let mut a = vec![k / 2; n];
            for _ in 0..n / 2 {
                prev(&mut a, k, n);
            }
            a
        }
    };
    println!(
        "{}",
        ans.iter()
            .map(|&x| (x + 1).to_string())
            .fold(String::new(), |acc, x| if acc.is_empty() {
                x
            } else {
                acc + " " + x.as_ref()
            })
    );
}