LR-remainders
Contest: Codeforces Round 927 (Div. 3)
Difficulty rating: 1400
Tags: brute force, data structures, implementation, math, two pointers

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).

Input format:
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 $$$2\cdot10^5$$$.

Output format:
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.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
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.

Example input:
4
4 6
3 1 4 2
LRRL
5 1
1 1 1 1 1
LLLLL
6 8
1 2 3 4 5 6
RLLLRR
1 10000
10000
R

Example output:
0 2 4 1 
0 0 0 0 0 
0 0 0 4 4 4 
0

Editorial:
If we perform all deletions except the last one, only one element will remain. Let's find its index in the array.
Now we will perform the operations in reverse order, then the deletion operations will become additions, which are much easier to maintain. We will store the remainder of the division of the product of the current segment by $$$m$$$ and multiply by the new elements when extending the segment. We will output all the obtained numbers in reverse order.