An array (b_1, b_2, \ldots, b_m) is good if, for each (i) ((1 \leq i \lt m)), (b_{i+1} \geq b_i) and (b_{i+1} - b_i \leq k). An array of length (1) is always good. You are given an initially good array (a_1, a_2, \ldots, a_n). Solve the following problem for each (i) ((1 \leq i \leq n)) independently : The (i)-th element of (a) is removed, making (a = a_1, a_2, \ldots, a_{i-1}, a_{i+1}, \ldots, a_n). In one operation, you are able to subtract (1) from any element of (a). What is the minimum number of operations required to make (a) good again? The first line of each input contains (t) ((1 \leq t \leq 10^4)) — the number of test cases. The first line of each test case contains two integers (n) and (k) ((2 \leq n \leq 2 \cdot 10^5, 1 \leq k \leq 10^9)). The second line of each test case contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \leq a_i \leq 10^9)). It is guaranteed that (a) is initially good. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output (n) space separated integers on a single line: the (i)-th integer denoting the solution to the problem for the (i)-th index. In the first test case: (i = 1), (a = 2, 4, 5). Since (a) is still good, we do not need to perform any operations. (i = 2), (a = 1, 4, 5). If we perform the operation once on the (2)nd element, (a = 1, 3, 5), which is a good array. (i = 3), (a = 1, 2, 5). If we perform the operation once on the (3)rd element, (a = 1, 2, 4), which is a good array. (i = 4), (a = 1, 2, 4). Since (a) is still good, we do not need to perform any operations. In the fourth test case, (a) will remain good no matter what element we remove, so the answer for each index is (0).