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.

1. $|S| \\lt |T|$ and $(S_1,S_2,\\ldots,S_{|S|}) = (T_1,T_2,\\ldots,T_{|S|})$.
2. 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:

$B_1$ $B_2$ $\\dots$ $B_N$

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