An array (b = b_1, b_2, \ldots, b_m) of length (m) is called (p)- towering if there exists an index (i) ((1\le i\le m)) such that for every index (j) ((1 \le j \le m)), the following condition holds: ()b_j \ge p - |i - j|.() Given an array (a = a_1, a_2, \ldots, a_n) of length (n), you can remove at most (k) elements from it. Determine the maximum value of (p) for which the remaining array can be made (p)- towering . 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) ((0 \le k < n \le 2 \cdot 10^5)). The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le 10^9)). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single integer — the maximum value of (p) for which the remaining array can be made (p)- towering . In the first test case, you cannot delete any element. The array remains (2, 1, 4, \color{red}{5}, 2) and is p-towering for (p = 3) by picking (i = 4): (a_1 = 2 \ge p - |i - 1| = 3 - |4 - 1| = 0); (a_2 = 1 \ge p - |i - 2| = 3 - |4 - 2| = 1); (a_3 = 4 \ge p - |i - 3| = 3 - |4 - 3| = 2); (a_4 = 5 \ge p - |i - 4| = 3 - |4 - 4| = 3); (a_5 = 2 \ge p - |i - 5| = 3 - |4 - 5| = 2). In the second test case, you can remove the first, second, and fifth elements to obtain the array (4, \color{red}{5}). Clearly, the obtained array is p-towering for (p = 5) by picking (i = 2).