Problem Statement

You are given positive integers $N$ and $K$.

An integer sequence of length $NK$ where each integer from $1$ to $N$ appears exactly $K$ times is called a good integer sequence.

Let $S$ be the number of good integer sequences. Find the $\operatorname{floor}((S+1)/2)$-th good integer sequence in lexicographical order. Here, $\operatorname{floor}(x)$ represents the largest integer not exceeding $x$.

What is lexicographical order for sequences? A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is lexicographically smaller than a sequence $T = (T_1,T_2,\ldots,T_{|T|})$ if either 1. or 2. below holds. Here, $|S|$ and $|T|$ represent the lengths of $S$ and $T$, respectively. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. There exists an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold: $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$ $S_i$ is (numerically) smaller than $T_i$.

Constraints

• $1 \leq N \leq 500$
• $1 \leq K \leq 500$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N K

Output

Print the desired integer sequence, with elements separated by spaces.