There exists an infinitely long number line. On the number line, there are (n) robots and (m) spikes, each located at a specific point on the number line. The (i)-th robot is located at position (a_i), and the (i)-th spike is located at position (b_i). If a robot touches a spike, it dies. (k) instructions are transmitted to the robots, with each instruction being to either move left by one unit or to move right by one unit. For each value (i) ((1 \leq i \leq k)), output how many robots are still alive after the first (i) instructions have been processed. The first line of the input contains a single 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, k) ((1 \le n, m, k \le 2 \cdot 10^5)) — the number of robots, spikes, and instructions respectively. The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((0 \le a_i \le 10^9)) — the locations of the robots. It is guaranteed that all elements of (a) are distinct. The third line contains (m) integers (b_1, b_2, \ldots, b_m) ((0 \le b_i \le 10^9)) — the locations of the spikes. It is guaranteed that all elements of (b) are distinct. The fourth line contains a string of length (k) — the instructions transmitted to the robots. Each character is either (L), representing an instruction to move to the left, or (R), representing an instruction to move to the right. It is guaranteed that the sum of each of (n, m, k) over all test cases does not exceed (2 \cdot 10^5). Additional constraint : it is guaranteed that there are no robots and spikes at the same position. Output (k) integers, where the (i)-th integer indicates how many robots are alive after the first (i) instructions have been processed. For Python users, make sure to select PyPy3 / PyPy2 (depending on which version of Python you're using) i