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:

~N\ K~

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