B'Dmitry has an array of n non-negative integers a_1, a_2, ... , a_n . In one operation, Dmitry can choose any index j ( 1 <= j <= n ) and increase the value of the element a_j by 1 . He can choose the same index j multiple times. For each i from 0 to n , determine whether Dmitry can make the mathrm{MEX} of the array equal to exactly i . If it is possible, then determine the minimum number of operations to do it. The mathrm{MEX} of the array is equal to the minimum non-negative integer that is not in the array. For example, the mathrm{MEX} of the array [3, 1, 0] is equal to 2 , and the array [3, 3, 1, 4] is equal to 0 . The first line of input data contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases in the input. The descriptions of the test cases follow. The first line of the description of each test case contains a single integer n ( 1 <= n <= 2 cdot 10^5 ) -- the length of the array a . The second line of the description of each test case contains n integers a_1, a_2, ... , a_n ( 0 <= a_i <= n ) -- elements of the array a . It is guaranteed that the sum of the values n over all test cases in the test does not exceed 2 cdot10^5 . For each test case, output n + 1 integer -- i -th number is equal to the minimum number of operations for which you can make the array mathrm{MEX} equal to i ( 0 <= i <= n ), or -1 if this cannot be done. In the first set of example inputs, n=3 : '...