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: On the first operation, the array changes from (1) to (0), since (\operatorname{MEX}(1) = 0). 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