B"There is an array a of size 2^k for some positive integer k , which is initially a permutation of values from 1 to 2^k . Alice and Bob play the following game on the array a . First, a value t between 1 and k is shown to both Alice and Bob. Then, for exactly t turns, the following happens: The score of the game is defined as the maximum value in a after all t turns have been played. Alice wants to maximize this score, while Bob wants to minimize it. You need to output k numbers: the score of the game if both Alice and Bob play optimally for t from 1 to k . Each test contains multiple test cases. The first line contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of the test cases follows. The first line of each test case contains an integer k ( 1 <= k <= 20 ) -- the parameter of the size of a . The second line of each test case contains 2^k integers a_1, a_2, ldots, a_{2^k} ( 1 <= a_i <= 2^k , a_i 's are pairwise distinct) -- the given array a . It is guaranteed that the sum of 2^k over all test cases does not exceed 2^{20} . For each test case, print k numbers, where the i -th number is the score of the game if both Alice and Bob play optimally for t = i . In the third test case, for t = 2 , the game could have proceeded as follows: "...