Array and Operations

You have an integer array $X$ of size $n$, initialized with all zeros. You will apply operations to this array $q$ times.

There are two kinds of operations.

• Add: add $i$ to every $X[i]$. ($0 \le i < n$)
• Reverse: a reverse operation needs two indices $i$ and $j$ with $i \le j$. It reverses the order of the elements from $X[i]$ through $X[j]$. That is, the order of $X[i], X[i+1], \ldots, X[j-1], X[j]$ is reversed.

For example, let $n = 6$ and consider applying the following five operations in order.

1. Add
2. Add
3. Reverse with $i = 0$, $j = 4$
4. Add
5. Reverse with $i = 2$, $j = 5$

Initially $X$ is $[0, 0, 0, 0, 0, 0]$. The result after each operation is as follows.

1. $[0, 1, 2, 3, 4, 5]$
2. $[0, 2, 4, 6, 8, 10]$
3. $[8, 6, 4, 2, 0, 10]$
4. $[8, 7, 6, 5, 4, 15]$
5. $[8, 7, 15, 4, 5, 6]$

Given the size $n$ of the array, the number $q$ of operations applied, and the operations themselves, you want to determine the values stored in $X$.

Given an array $Y$ of size $m$, find the value of $X[Y[i]]$ after all operations have been applied.

The first line contains three integers $n$, $q$, $m$. ($1 \le n \le 1{,}000{,}000$, $0 \le q \le 10{,}000$, $1 \le m \le 5{,}000$)

The next $q$ lines contain the operations, one per line. Each line starts with 'a' or 'r'. 'a' denotes an add operation and 'r' denotes a reverse operation. When the line starts with 'r', it is followed by two space-separated integers $i$ and $j$. ($0 \le i \le j < n$)

The last line contains $m$ integers that describe the array $Y$, in order. ($0 \le Y[i] < n$)

Print the value of $X[Y[i]]$ on each of $m$ lines, one per line, in order.