Solve the programming task below in a Python markdown code block.
Given an array $a$ of length $n$, you can do at most $k$ operations of the following type on it:

choose $2$ different elements in the array, add $1$ to the first, and subtract $1$ from the second. However, all the elements of $a$ have to remain non-negative after this operation.

What is lexicographically the smallest array you can obtain?

An array $x$ is lexicographically smaller than an array $y$ if there exists an index $i$ such that $x_i<y_i$, and $x_j=y_j$ for all $1 \le j < i$. Less formally, at the first index $i$ in which they differ, $x_i<y_i$.


-----Input-----

The first line contains an integer $t$ ($1 \le t \le 20$) – the number of test cases you need to solve.

The first line of each test case contains $2$ integers $n$ and $k$ ($2 \le n \le 100$, $1 \le k \le 10000$) — the number of elements in the array and the maximum number of operations you can make.

The second line contains $n$ space-separated integers $a_1$, $a_2$, $\ldots$, $a_{n}$ ($0 \le a_i \le 100$) — the elements of the array $a$.


-----Output-----

For each test case, print the lexicographically smallest array you can obtain after at most $k$ operations.


-----Examples-----

Input
2
3 1
3 1 4
2 10
1 0
Output
2 1 5 
0 1


-----Note-----

In the second test case, we start by subtracting $1$ from the first element and adding $1$ to the second. Then, we can't get any lexicographically smaller arrays, because we can't make any of the elements negative.