B'Farmer John has a permutation p_1, p_2, ldots, p_n , where every integer from 0 to n-1 occurs exactly once. He gives Bessie an array a of length n and challenges her to construct p based on a . The array a is constructed so that a_i = texttt{MEX}(p_1, p_2, ldots, p_i) - p_i , where the texttt{MEX} of an array is the minimum non-negative integer that does not appear in that array. For example, texttt{MEX}(1, 2, 3) = 0 and texttt{MEX}(3, 1, 0) = 2 . Help Bessie construct any valid permutation p that satisfies a . The input is given in such a way that at least one valid p exists. If there are multiple possible p , it is enough to print one of them. The first line contains t ( 1 <= q t <= q 10^4 ) -- the number of test cases. The first line of each test case contains an integer n ( 1 <= q n <= q 2 cdot 10^5 ) -- the lengths of p and a . The second line of each test case contains n integers a_1, a_2, ldots, a_n ( -n <= q a_i <= q n ) -- the elements of array a . It is guaranteed that there is at least one valid p for the given data. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output n integers on a new line, the elements of p . If there are multiple solutions, print any of them. In the first case, p = [0, 1, 4, 2, 3] is one possible output. a will then be calculated as a_1 = texttt{MEX}(0) - 0 = 1 , a_2 = texttt{MEX}(0, 1) - 1 = 1 , a_3 = texttt{MEX}(0, 1, 4) - 4 = -2 , a_4 = texttt{MEX}(0, 1, 4, 2) - 2 = 1 , a_5 = texttt{MEX}(0, 1, 4, 2, 3) - 3 = 2 . So, as required, a will be [1, 1, -2, 1, 2] . '...