You are given an integer (k) and an array (a) of length (n), where each element satisfies (0 \le a_i \le k) for all (1 \le i \le n). You can perform the following operation on the array: Choose two distinct indices (i) and (j) ((1 \le i,j \le n) and (i \neq j)) such that (a_i + a_j = k). Select an integer (x) satisfying (-a_j \le x \le a_i). Decrease (a_i) by (x) and increase (a_j) by (x). In other words, update (a_i := a_i - x) and (a_j := a_j + x). Note that the constraints on (x) ensure that all elements of array (a) remain between (0) and (k) throughout the operations. Your task is to determine whether it is possible to make the array (a) non-decreasing(^{\text{∗}}) using the above operation. If it is possible, find a sequence of at most (3n) operations that transforms the array into a non-decreasing one. It can be proven that if it is possible to make the array non-decreasing using the above operation, there exists a solution that uses at most (3n) operations. (^{\text{∗}}) An array (a_1, a_2, \ldots, a_n) is said to be non-decreasing if for all (1 \le i \le n - 1), it holds that (a_i \le a_{i+1}). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains two integers, (n) and (k) ((4 \le n \le 2 \cdot 10^5), (1 \le k \le 10^9)) — the length of the array (a) and the required sum for the operation. The second line of each test case contains (n) integers (a_1, a_2, \ldots, a_n) ((0 \le a_i \le k)) — the elements of array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output (-1) if it is not possible to make the array non-decreasing using the operation. Otherwise, output the