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문제

Byteasar has learnt a fabulous recursive method of shuffling a deck of cards. This algorithm can be described as follows:

  • In order to shuffle two cards, swap them.
  • In order to shuffle $2^k$ cards ($k \geq 2$), split them into two equal parts -- an upper one and a lower one (so that each of them has $2^{k - 1}$ cards). Shuffle each of them recursively and then put the lower half on the top of the upper half.

Byteasar has a deck of $2^n$ cards. Each of them has a number written on it. Byteasar now shuffles the deck, running the procedure described above exactly $t$ times. As it might take a great amount of time, he would like to know the final order of the cards beforehand.

입력

The first line of the input contains two integers $n, t$ ($1 \le n \le 20$, $1 \le t \le 10^9$). The second line contains $2^n$ integers $a_1, \dots, a_{2^n}$ ($1 \le a_i \le 10^9$); $a_i$ is the number written on the $i$-th topmost card in the deck.

출력

In the first and only line of output print $2^n$ integers -- the numbers written on the cards of Byteasar's deck after $t$ shuffles. Print the numbers in the order from the topmost to the bottommost card.

예제 입력 1

2 1
2 4 1 5

예제 출력 1

5 1 4 2