Napoleon Cake

1000ms

262144K

Description:

This week Arkady wanted to cook some pancakes (to follow ancient traditions) and make a problem about that. But then he remembered that one can't make a problem about stacking pancakes without working at a specific IT company, so he decided to bake the Napoleon cake instead.

To bake a Napoleon cake, one has to bake $$$n$$$ dry layers first, and then put them on each other in one stack, adding some cream. Arkady started with an empty plate, and performed the following steps $$$n$$$ times:

place a new cake layer on the top of the stack;
after the $$$i$$$-th layer is placed, pour $$$a_i$$$ units of cream on top of the stack.

When $$$x$$$ units of cream are poured on the top of the stack, top $$$x$$$ layers of the cake get drenched in the cream. If there are less than $$$x$$$ layers, all layers get drenched and the rest of the cream is wasted. If $$$x = 0$$$, no layer gets drenched.

$\text{[math]}$ The picture represents the first test case of the example.

Help Arkady determine which layers of the cake eventually get drenched when the process is over, and which don't.

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 20\,000$$$). Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of layers in the cake.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le n$$$) — the amount of cream poured on the cake after adding each layer.

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

Output:

For each test case, print a single line with $$$n$$$ integers. The $$$i$$$-th of the integers should be equal to $$$1$$$ if the $$$i$$$-th layer from the bottom gets drenched, and $$$0$$$ otherwise.

Sample Input:

3
6
0 3 0 0 1 3
10
0 0 0 1 0 5 0 0 0 2
3
0 0 0

Sample Output:

1 1 0 1 1 1 
0 1 1 1 1 1 0 0 1 1 
0 0 0

Informação

Provedor Codeforces

Código CF1501B