CF1863C MEX Repetition

You are given an array $ a_1,a_2,\ldots, a_n $ of pairwise distinct integers from $ 0 $ to $ n $ . Consider the following operation: - consecutively for each $ i $ from $ 1 $ to $ n $ in this order, replace $ a_i $ with $ \operatorname{MEX}(a_1, a_2, \ldots, a_n) $ . Here $ \operatorname{MEX} $ of a collection of integers $ c_1, c_2, \ldots, c_m $ is defined as the smallest non-negative integer $ x $ which does not occur in the collection $ c $ . For example, $ \operatorname{MEX}(0, 2, 2, 1, 4) = 3 $ and $ \operatorname{MEX}(1, 2) = 0 $ . Print the array after applying $ k $ such operations.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^5 $ ). The description of the test cases follows. The first line of each test case contains two integers $ n $ and $ k $ ( $ 1\le n\le 10^5 $ , $ 1\le k\le 10^9 $ ). The second line contains $ n $ pairwise distinct integers $ a_1,a_2,\ldots, a_n $ ( $ 0\le a_i\le n $ ) representing the elements of the array before applying the operations. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, print all $ n $ elements of the array after applying $ k $ operations.

In the first test case, here is the entire process: 1. On the first operation, the array changes from $ [1] $ to $ [0] $ , since $ \operatorname{MEX}(1) = 0 $ . 2. On the second operation, the array changes from $ [0] $ to $ [1] $ , since $ \operatorname{MEX}(0) = 1 $ . Thus, the array becomes $ [1] $ after two operations. In the second test case, the array changes as follows during one operation: $ [{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 1, 3] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 3] \rightarrow [2, 0, {\mkern3mu\underline{\mkern-3mu {\bf 3}\mkern-3mu}\mkern3mu}] \rightarrow [2, 0, 1] $ . In the third test case, the array changes as follows during one operation: $ [{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 2] \rightarrow [1, {\mkern3mu\underline{\mkern-3mu {\bf 2}\mkern-3mu}\mkern3mu}] \rightarrow [1, 0] $ . And during the second operation: $ [{\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 0] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}] \rightarrow [2, 1] $ .