Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] 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 ------
$1 ≤ T ≤ 1,000$
$1 ≤ N, Z ≤ 10^{6}$
$0 ≤ A_{i} ≤ 1$ for each valid $i$
the sum of $N$ over all test cases does not exceed $10^{6}$

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

Subtask #2 (90 points): original constraints

----- Sample Input 1 ------
2

6 2

0 1 1 0 1 1

4 4

0 1 0 1
----- Sample Output 1 ------
1 1 0 1 1 0

1 1 0 0
----- explanation 1 ------
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 $(1, 1, 0, 0)$.

见题面

见题面