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).

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:
$B_1 B_2 \dots B_N$

Constraints

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

Sample Input 1

3 5
1 3 2

Sample Output 1

2 3 1

Here are the permutations f(L, R) for all pairs (L, R) such that $1 \leq L \leq R \leq N$.

• f(1, 1) = (1, 3, 2)
• f(1, 2) = (3, 1, 2)
• f(1, 3) = (2, 3, 1)
• f(2, 2) = (1, 3, 2)
• f(2, 3) = (1, 2, 3)
• f(3, 3) = (1, 3, 2)

When these are sorted in lexicographical order, the fifth permutation is f(1, 3) = (2, 3, 1), which should be printed.

Sample Input 2

5 15
1 2 3 4 5

Sample Output 2

5 4 3 2 1

The answer is f(1, 5).

Sample Input 3

10 37
9 2 1 3 8 7 10 4 5 6

Sample Output 3

9 2 1 6 5 4 10 7 8 3

见题面 Input 部分

见题面 Output 部分