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B. Collecting Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ of $$$n$$$ positive integers and a score. If your score is greater than or equal to $$$a_i$$$, then you can increase your score by $$$a_i$$$ and remove $$$a_i$$$ from the array.

For each index $$$i$$$, output the maximum number of additional array elements that you can remove if you remove $$$a_i$$$ and then set your score to $$$a_i$$$. Note that the removal of $$$a_i$$$ should not be counted in the answer.

Input

Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 5000$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of the array.

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

Output

For each test case, output $$$n$$$ integers, the $$$i$$$-th of which denotes the maximum number of additional array elements that you can remove if you remove $$$a_i$$$ from the array and then set your score to $$$a_i$$$.

Example
Input
4
5
20 5 1 4 2
3
1434 7 1442
1
1
5
999999999 999999999 999999999 1000000000 1000000000
Output
4 3 0 3 1 
1 0 2 
0 
4 4 4 4 4
Note

In the first test case, the answers are as follows:

If we start with $$$i=4$$$, our initial score is $$$a_4=4$$$ and $$$a=[20,5,1,2]$$$. We can remove $$$3$$$ additional elements in the following order:

  1. Since $$$4 \ge 1$$$, we can remove $$$1$$$ and our score becomes $$$5$$$. After this, $$$a=[20,5,2]$$$.
  2. Since $$$5 \ge 5$$$, we can remove $$$5$$$ and our score becomes $$$10$$$. After this, $$$a=[20,2]$$$.
  3. Since $$$10 \ge 2$$$, we can remove $$$2$$$ and our score becomes $$$12$$$. After this, $$$a=[20]$$$.

If we start with $$$i=1$$$ we can remove all remaining elements in the array, so the answer is $$$4$$$.

If we start with $$$i=2$$$, we can remove $$$3$$$ additional elements in the following order: $$$1$$$, $$$4$$$, $$$2$$$.

If we start with $$$i=3$$$, we can remove no additional elements.

If we start with $$$i=5$$$, we can remove $$$1$$$ additional element: $$$1$$$.