B"Let's define f(S) . Let S be a multiset (i.e., it can contain repeated elements) of non-negative integers. In one operation, you can choose any non-empty subset of S (which can also contain repeated elements), remove this subset (all elements in it) from S , and add the MEX of the removed subset to S . You can perform any number of such operations. After all the operations, S should contain exactly 1 number. f(S) is the largest number that could remain in S after any sequence of operations. You are given an array of non-negative integers a of length n . For each of its n prefixes, calculate f(S) if S is the corresponding prefix (for the i -th prefix, S consists of the first i elements of array a ). The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance: The first line contains a single integer t ( 1 <= q t <= q 10^4 ) -- the number of test cases. Then follows the description of the test cases. The first line of each test case contains an integer n ( 1 <= q n <= q 2 cdot 10^5 ) -- the size of array a . The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 0 <= q a_i <= q 2 cdot 10^5 ) -- the array a . It is guaranteed that the sum of all n values across all test cases does not exceed 2 cdot 10^5 . For each test case, output n numbers: f(S) for each of the n prefixes of array a . Consider the first test case. For a prefix of length 1 , the initial multiset is {179 } . If we do nothing, we get 179 . For a prefix of length 2 , the initial multiset is {57, 179 } . Using the following sequence of operations, we can obtain 2 . Consider the second test case. For a prefix of length 1 , the initial multiset is {0 } . If we apply the operation to "...