2017 Winter Waterloo Local ACM Contest, Problem C

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

$${\displaystyle H(x_1,\dots ,x_N)={\left(\frac{\sum _{i=1}^N{x}_i^{-1}}{N}\right)}^{-1}}$$

Vera classifies an array of positive integers $A=[A_1,\dots ,A_N]$ of length $N$ as $K$-mean-sorted if $M(i)\ge M(i+1)$ for $1\le i\le N-K$ where

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

A permutation $P$ is an ordered set of integers $P_1,P_2,\dots ,P_N$, consisting of $N$ distinct positive integers, each of which are at most $N$.

Permutation $P$ is lexicographically smaller than permutation $Q$ if there is $i$ ($1\le i\le n$), such that $P_i<Q_i$, and for any $j$ ($1\le j<i$) $P_j=Q_j$.

Given integers $N$ and $K$, help Vera find the lexicographically smallest permutation $P$ of integers $1$ to $N$ such that $P$ is $K$-mean-sorted but not $L$-mean-sorted for $1\le L\le N-1$, $L\ne K$.

If no such permutation exists, output 0.

Constraints

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

Input Specification

The input will be in the format:

$NK$

Output Specification

Output one line with the desired permutation. If such permutation does not exist, output one line with 0.

Sample Input 1

3 2

Sample Output 1

2 3 1

Sample Input 2

4 1

Sample Output 2

0