D. Prefix Purchase
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You have an array $$$a$$$ of size $$$n$$$, initially filled with zeros ($$$a_1 = a_2 = \ldots = a_n = 0$$$). You also have an array of integers $$$c$$$ of size $$$n$$$.

Initially, you have $$$k$$$ coins. By paying $$$c_i$$$ coins, you can add $$$1$$$ to all elements of the array $$$a$$$ from the first to the $$$i$$$-th element ($$$a_j \mathrel{+}= 1$$$ for all $$$1 \leq j \leq i$$$). You can buy any $$$c_i$$$ any number of times. A purchase is only possible if $$$k \geq c_i$$$, meaning that at any moment $$$k \geq 0$$$ must hold true.

Find the lexicographically largest array $$$a$$$ that can be obtained.

An array $$$a$$$ is lexicographically smaller than an array $$$b$$$ of the same length if and only if in the first position where $$$a$$$ and $$$b$$$ differ, the element in array $$$a$$$ is smaller than the corresponding element in $$$b$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. This is followed by a description of the test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the size of arrays $$$a$$$ and $$$c$$$.

The second line of each test case contains $$$n$$$ integers $$$c_1, c_2, \ldots, c_n$$$ ($$$1 \leq c_i \leq 10^9$$$) — the array $$$c$$$.

The third line of each test case contains a single integer $$$k$$$ ($$$1 \leq k \leq 10^9$$$) — the number of coins you have.

It is guaranteed that the sum of all $$$n$$$ values across all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ — the lexicographically largest array $$$a$$$ that can be obtained.

Example
Input
4
3
1 2 3
5
2
3 4
7
3
3 2 1
2
6
10 6 4 6 3 4
7
Output
5 0 0 
2 1 
2 2 2 
2 2 2 2 2 1
Note

In the first test case, $$$a_1$$$ cannot be greater than $$$5$$$, and if we buy $$$c_1$$$ five times, we will run out of money, so $$$a = [5, 0, 0]$$$.

In the second test case, $$$a_1$$$ cannot be greater than $$$2$$$, but we can buy $$$c_1$$$ and $$$c_2$$$ once each (buying $$$c_2$$$ twice is not possible), so $$$a = [2, 1]$$$.