Let (n, m, \ell) be positive integers. You have made the unfortunate decision to work as a night guard at Freddy Fazbear's Pizzeria, where there are (m) animatronics numbered (1, \ldots, m) waiting to jumpscare you. The night consists of (\ell) seconds, numbered (1, \ldots, \ell). The (j)-th of the (m) animatronics has a danger level (d_j), and initially (d_1 = \ldots = d_m = 0). Every second, the danger level of exactly one animatronic will increase by (1), and throughout the night, you are able to observe all values of (d_j) at the current time. For example, if (m = 2), one possible list of danger levels after (5) seconds is (d_1, d_2 = 2, 3). You are not defenseless, however. At each of the (n) fixed times (a_i) ((1 \leq a_1 \lt \ldots \lt a_n \leq \ell)), you can shine your flashlight on exactly one animatronic (j_i) of your choice. This occurs immediately after the (a_i)-th second and sets its danger level back to zero, i.e. (d_{j_i} := 0). Note that this choice is made independently for each flashlight use (a_i). Continuing the example from before, if (a_1 = 5) and you choose to flash the second animatronic at that time, the danger levels after (5) seconds will be (d_1, d_2 = 2, 0). Let the overall danger be the maximum danger across all animatronics, i.e. (\max_{1 \leq j \leq m} d_j). You will lose if the overall danger at the end of the night (after (\ell) seconds) is greater than (x). Find the minimum value of (x) such that regardless of the actions of the animatronics, you can guarantee that overall danger will be less than or equal (x). 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 three integers (n), (m), and (\ell) ($$$1 \leq n, m, \ell \leq 2 \cdot 1