15441번 - Vera and Mean Sorting 다국어

문제

The harmonic mean of a sequence of positive integers x₁, · · · , x_N is

\[H\left(x_1, \cdots, x_N\right) = \left( \frac{\sum_{i=1}^{N}{x_i^{-1}}}{N}\right)^{-1} \text{.}\]

Vera classifies an array of positive integers A = [A₁, · · · , A_N] of length N as K-mean-sorted if M(i) ≥ M(i + 1) for 1 ≤ i ≤ N − K where

\[M\left(i\right) = H\left(A_i, \cdots, A_{i+K-1}\right) \text{.}\]

A permutation P is an ordered set of integers P₁, P₂, · · · , 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 an i (1 ≤ i ≤ N), such that P_i < Q_i, and for any j (1 ≤ 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 ≤ L ≤ N − 1, L ≠ K.

If no such permutation exists output 0.

입력

The input will be in the format:

N K

Constraints:

• 2 ≤ N ≤ 100
• 1 ≤ K ≤ N − 1
• N, K are integers

출력

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

제한

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