200842: [AtCoder]ARC084 E - Finite Encyclopedia of Integer Sequences

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