Collecting Game
Description
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.
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 $10^5$.
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 $a_i$.
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 $a_i$.
4
5
20 5 1 4 2
3
1434 7 1442
1
1
5
999999999 999999999 999999999 1000000000 1000000000
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:
- Since $4 \ge 1$, we can remove $1$ and our score becomes $5$. After this, $a=[20,5,2]$.
- Since $5 \ge 5$, we can remove $5$ and our score becomes $10$. After this, $a=[20,2]$.
- 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: $1$.