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 $$$x_i \lt y_i$$$, and $$$x_j=y_j$$$ for all $$$1 \le j \lt i$$$. Less formally, at the first index $$$i$$$ in which they differ, $$$x_i \lt y_i$$$.

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.

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.

Tit for Tat

Examples