Problem Statement

You are given a permutation $A = (A_1, A_2, \dots, A_N)$ of $(1, 2, \dots, N)$. For a pair of integers $(L, R)$ such that $1 \leq L \leq R \leq N$, let $f(L, R)$ be the permutation obtained by reversing the $L$-th through $R$-th elements of $A$, that is, replacing $A_L, A_{L+1}, \dots, A_{R-1}, A_R$ with $A_R, A_{R-1}, \dots, A_{L+1}, A_{L}$ simultaneously.

There are $\frac{N(N + 1)}{2}$ ways to choose $(L, R)$ such that $1 \leq L \leq R \leq N$. If the permutations $f(L, R)$ for all such pairs $(L, R)$ are listed and sorted in lexicographical order, what is the $K$-th permutation from the front?

What is lexicographical order on sequences? A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is said to be lexicographically smaller than a sequence $T = (T_1,T_2,\ldots,T_{|T|})$ if and only if 1. or 2. below holds. Here, $|S|$ and $|T|$ denote 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 is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ that satisfies both of the following. $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$. $S_i$ is smaller than $T_i$ (as a number).

Constraints

• $1 \leq N \leq 7000$
• $1 \leq K \leq \frac{N(N + 1)}{2}$
• $A$ is a permutation of $(1, 2, \dots, N)$.

Input

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

N K
A_1 A_2 \dots A_N

Output

Let $B =(B_1, B_2, \dots, B_N)$ be the $K$-th permutation from the front in the list of the permutations $f(L, R)$ sorted in lexicographical order. Print $B$ in the following format:

B_1 B_2 \dots B_N