CF1932C.LR-remainders

You are given an array $a$ of length $n$ , a positive integer $m$ , and a string of commands of length $n$ . Each command is either the character 'L' or the character 'R'.

Process all $n$ commands in the order they are written in the string $s$ . Processing a command is done as follows:

• First, output the remainder of the product of all elements of the array $a$ when divided by $m$ .
• Then, if the command is 'L', remove the leftmost element from the array $a$ , if the command is 'R', remove the rightmost element from the array $a$ .

Note that after each move, the length of the array $a$ decreases by $1$ , and after processing all commands, it will be empty.

Write a program that will process all commands in the order they are written in the string $s$ (from left to right).

The first line contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the input. Then descriptions of $t$ test cases follow.

Each test case of the input is given by three lines.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 2\cdot10^5, 1 \le m \le 10^4$ ) — the initial length of the array $a$ and the value to take the remainder by.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^4$ ) — the elements of the array $a$ .

The third line contains a string $s$ consisting of $n$ characters 'L' and 'R'.

It is guaranteed that the sum of the values of $n$ for all test cases in a test does not exceed $2\cdot10^5$ .

For each test case, output $n$ integers $b_1, b_2, \dots, b_n$ , where $b_i$ is the remainder when dividing the product of all elements of the current state of the array $a$ by $m$ at the beginning of the execution of the $i$ -th command.

In the first test case of the example:

• $3 \cdot 1 \cdot 4 \cdot 2 \bmod 6 = 24 \bmod 6 = 0$ ;
• $s_1 = \text{L}$ , so we remove the first element and get the array $[1, 4, 2]$ ;
• $1 \cdot 4 \cdot 2 \bmod 6 = 8 \bmod 6 = 2$ ;
• $s_2 = \text{R}$ , so we remove the last element and get the array $[1, 4]$ ;
• $1 \cdot 4 \bmod 6 = 4 \bmod 6 = 4$ ;
• $s_3 = \text{R}$ , so we remove the last element and get the array $[1]$ ;
• $1 \bmod 6 = 1$ ;
• $s_4 = \text{L}$ , so we remove the first element and get an empty array.