CF1870D.Prefix Purchase

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 $b$ .

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 $2 \cdot 10^5$ .

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

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 $a = [2, 1]$ .