Vera and Mean Sorting

The harmonic mean of a sequence of positive integers $x_1, x_2, \dots, x_N$ is

$H(x_1, \dots, x_N) = \left( \frac{\sum_{i=1}^{N} x_i^{-1}}{N} \right)^{-1}$

For an array of positive integers $A = [A_1, \dots, A_N]$ of length $N$, let

$M(i) = H(A_i, A_{i+1}, \dots, A_{i+K-1})$

Vera calls $A$ $K$-mean-sorted if $M(i) \ge M(i+1)$ holds for every $i$ with $1 \le i \le N - K$.

A permutation $P$ is an ordered list of $N$ distinct positive integers $P_1, P_2, \dots, P_N$, each of them at most $N$.

Permutation $P$ is lexicographically smaller than permutation $Q$ if there is an $i$ ($1 \le i \le N$) with $P_i < Q_i$ such that $P_j = Q_j$ for every $j$ with $1 \le j < i$.

You are given the integers $N$ and $K$. Among the permutations $P$ of the integers $1$ through $N$ that are $K$-mean-sorted and are not $L$-mean-sorted for any $L$ ($1 \le L \le N - 1$) with $L \ne K$, help Vera find the lexicographically smallest one. If no such permutation exists, print $0$.

The input is given in the following format.

N K

Constraints:

• $2 \le N \le 100$
• $1 \le K \le N - 1$
• $N$ and $K$ are integers.

Print the permutation on one line, with the numbers separated by single spaces. If no such permutation exists, print $0$ on one line.