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