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 (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, BinaryHeap};
#[allow(unused_imports)]
use std::iter::FromIterator;

mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;

    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn get<T: FromStr>() -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    }

    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }

    #[allow(dead_code)]
    pub fn get2<T: FromStr, U: FromStr>() -> (T, U)
    where
        <T as FromStr>::Err: Debug,
        <U as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    }

    #[allow(dead_code)]
    pub fn get3<S: FromStr, T: FromStr, U: FromStr>() -> (S, T, U)
    where
        <S as FromStr>::Err: Debug,
        <T as FromStr>::Err: Debug,
        <U as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    }
}

#[allow(unused_macros)]
macro_rules! debug {
    ($x: expr) => {
        println!("{}: {:?}", stringify!($x), $x)
    }
}

fn main() {
    let (k, n): (usize, usize) = util::get2();

    if k % 2 == 0 {
        println!(
            "{}",
            vec![(k / 2).to_string()]
                .into_iter()
                .chain((1..n).map(|_| k.to_string()))
                .collect::<Vec<_>>()
                .join(" ")
        );
    } else {
        let mut v = vec![1 + k / 2; n];
        for _ in 0..n / 2 {
            let mut i = 0;
            loop {
                v[i] = ((k + 1) + v[i] - 1) % (k + 1);
                if v[i] != k {
                    break;
                }
                i += 1;
            }
        }

        println!(
            "{}",
            v.iter()
                .filter(|&&x| x != 0)
                .rev()
                .map(|x| x.to_string())
                .collect::<Vec<_>>()
                .join(" ")
        );
    }

}