A14196. Tit for Tat

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](https://en.wikipedia.org/wiki/Lexicographical_order) 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, $x_i<y_i$ .

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 $a$ .

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

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.