You have obtained the new limited event character Xilonen. You decide to use her in combat. There are (n) enemies in a line. The (i)'th enemy from the left has health (h_i) and is currently at position (x_i). Xilonen has an attack damage of (m), and you are ready to defeat the enemies with her. Xilonen has a powerful "ground stomp" attack. Before you perform any attacks , you select an integer (p) and position Xilonen there ((p) can be any integer position, including a position with an enemy currently). Afterwards, for each attack, she deals (m) damage to an enemy at position (p) (if there are any), (m-1) damage to enemies at positions (p-1) and (p+1), (m-2) damage to enemies at positions (p-2) and (p+2), and so on. Enemies that are at least a distance of (m) away from Xilonen take no damage from attacks. Formally, if there is an enemy at position (x), she will deal (\max(0,m - |p - x|)) damage to that enemy each hit. Note that you may not choose a different (p) for different attacks. Over all possible (p), output the minimum number of attacks Xilonen must perform to defeat at least (k) enemies. If it is impossible to find a (p) such that eventually at least (k) enemies will be defeated, output (-1) instead. Note that an enemy is considered to be defeated if its health reaches (0) or below. The first line contains an integer (t) ((1 \leq t \leq 10^4)) – the number of test cases. The first line of each test case contains three integers (n), (m), and (k) ((1 \leq k \leq n \leq 10^5), (1 \leq m \leq 10^9)). The following line contains (n) integers (h_1, h_2, ..., h_n) ((1 \leq h_i \leq 10^9)). The last line of each testcase contains (n) integers (x_1, x_2, ..., x_n) ((1\leq x_i \leq 10^9), (x_i < x_{i+1}) for all (1 \leq i < n)) It is guaranteed that the sum of (n) over all test cases does not exce