B. Collecting Gametime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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.OutputFor 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.ExampleInput
4520 5 1 4 231434 7 1442115999999999 999999999 999999999 1000000000 1000000000Output
4 3 0 3 1 
1 0 2 
0 
4 4 4 4 4 
NoteIn 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.
4520 5 1 4 231434 7 1442115999999999 999999999 999999999 1000000000 1000000000
4 3 0 3 1  1 0 2  0  4 4 4 4 4  
['binary search', 'dp', 'greedy', 'sortings', 'two pointers', '*1100']