B"Suppose you had an array A of n elements, each of which is 0 or 1 . Let us define a function f(k,A) which returns another array B , the result of sorting the first k elements of A in non-decreasing order. For example, f(4,[0,1,1,0,0,1,0]) = [0,0,1,1,0,1,0] . Note that the first 4 elements were sorted. Now consider the arrays B_1, B_2, ldots, B_n generated by f(1,A), f(2,A), ldots,f(n,A) . Let C be the array obtained by taking the element-wise sum of B_1, B_2, ldots, B_n . For example, let A=[0,1,0,1] . Then we have B_1=[0,1,0,1] , B_2=[0,1,0,1] , B_3=[0,0,1,1] , B_4=[0,0,1,1] . Then C=B_1+B_2+B_3+B_4=[0,1,0,1]+[0,1,0,1]+[0,0,1,1]+[0,0,1,1]=[0,2,2,4] . You are given C . Determine a binary array A that would give C when processed as above. It is guaranteed that an array A exists for given C in the input. The first line contains a single integer t ( 1 <= q t <= q 1000 ) -- the number of test cases. Each test case has two lines. The first line contains a single integer n ( 1 <= q n <= q 2 cdot 10^5 ). The second line contains n integers c_1, c_2, ldots, c_n ( 0 <= q c_i <= q n ). It is guaranteed that a valid array A exists for the given C . The sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output a single line containing n integers a_1, a_2, ldots, a_n ( a_i is 0 or 1 ). If there are multiple answers, you may output any of them. Here's the explanation for the first test case. Given that A=[1,1,0,1] , we can construct each B_i : "...