github.com/captn3m0/codechef.git

---
{"category_name":"medium","problem_code":"BINARY","problem_name":"Binary Movements","languages_supported":{"0":"C","1":"CPP14","2":"JAVA","3":"PYTH","4":"PYTH 3.6","5":"PYPY","6":"CS2","7":"PAS fpc","8":"PAS gpc","9":"RUBY","10":"PHP","11":"GO","12":"NODEJS","13":"HASK","14":"rust","15":"SCALA","16":"swift","17":"D","18":"PERL","19":"FORT","20":"WSPC","21":"ADA","22":"CAML","23":"ICK","24":"BF","25":"ASM","26":"CLPS","27":"PRLG","28":"ICON","29":"SCM qobi","30":"PIKE","31":"ST","32":"NICE","33":"LUA","34":"BASH","35":"NEM","36":"LISP sbcl","37":"LISP clisp","38":"SCM guile","39":"JS","40":"ERL","41":"TCL","42":"kotlin","43":"PERL6","44":"TEXT","45":"SCM chicken","46":"PYP3","47":"CLOJ","48":"R","49":"COB","50":"FS"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"iamabjain","problem_tester":null,"date_added":"18-04-2019","tags":{"0":"iamabjain"},"time":{"view_start_date":1557739980,"submit_start_date":1557739980,"visible_start_date":1557739980,"end_date":1735669800},"is_direct_submittable":false,"layout":"problem"}
---
<span class="solution-visible-txt">All submissions for this problem are available.</span>### Read problem statements in [Hindi](http://www.codechef.com/download/translated/MAY19/hindi/BINARY.pdf), [Bengali](http://www.codechef.com/download/translated/MAY19/bengali/BINARY.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/MAY19/mandarin/BINARY.pdf), [Russian](http://www.codechef.com/download/translated/MAY19/russian/BINARY.pdf), and [Vietnamese](http://www.codechef.com/download/translated/MAY19/vietnamese/BINARY.pdf) as well.

"Out of 6 billion humans, the troublemakers are just a handful." - Dalai Lama

Nikitasha and Mansi are best friends. They have a binary sequence $A_1, A_2, \ldots, A_N$ (each element of this sequence is $0$ or $1$). Their friend Sakshi always finds ways to trouble them. This time, Sakshi altered their sequence by performing the following operation $Z$ times:
- Create a new sequence $B_1, B_2, \ldots, B_N$. Initially, $A_i = B_i$ for each valid $i$.
- For each valid $i$ such that $A_i = 0$ and $A_{i+1} = 1$, swap $B_i$ and $B_{i+1}$, i.e. set $B_i = 1$ and $B_{i+1} = 0$. Note that the order of swaps does not matter.
- Replace the sequence $A$ by the sequence $B$.

Now, Sakshi challenges Nikitasha And Mansi to find the altered sequence (the resulting sequence $A$ after $Z$ steps). Help Nikitasha and Mansi find this sequence.

### Input
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $Z$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

### Output
For each test case, print a single line containing $N$ space-separated integers — the altered sequence.

### Constraints 
- $1 \le T \le 1,000$
- $1 \le N, Z \le 10^6$
- $0 \le A_i \le 1$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

### Subtasks
**Subtask #1 (10 points):**
- $1 \le N, Z \le 3,000$
- the sum of $N$ over all test cases does not exceed $3,000$

**Subtask #2 (90 points):** original constraints

### Example Input
```
2
6 2
0 1 1 0 1 1
4 4
0 1 0 1
```

### Example Output
```
1 1 0 1 1 0 	
1 1 0 0
```

### Explanation
**Example case 1:** After the first step, the sequence becomes $(1, 0, 1, 1, 0, 1)$. After the second step, it becomes $(1, 1, 0, 1, 1, 0)$.

**Example case 2:** After the first step, the sequence becomes $(1, 0, 1, 0)$. After the second step, the sequence becomes $(1, 1, 0, 0)$. Applying more steps does not alter the sequence anymore, so after the third and fourth step, the sequence remains $(1, 1, 0, 0)$.