Bubble Sort Rounds II

Bubble sort is a sorting algorithm that consists of a number of rounds. On each round the algorithm scans the array from left to right and swaps any adjacent elements that are in the wrong order. Given an array of n integers, find out the contents of the array after k bubble sort rounds.

Input

The first line has two integers n and k: the array size and the number of rounds. The next line has n integers x_1,x_2,\dots,x_n: the array contents.

Output

Print n integers: the contents of the array after k rounds.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$0 \le k \le 10^9$

$1 \le x_i \le 10^9$

Example

Input

5 2
3 2 4 1 4

Output

2 1 3 4 4