CF1705C.Mark and His Unfinished Essay

One night, Mark realized that there is an essay due tomorrow. He hasn't written anything yet, so Mark decided to randomly copy-paste substrings from the prompt to make the essay.

More formally, the prompt is a string $s$ of initial length $n$ . Mark will perform the copy-pasting operation $c$ times. Each operation is described by two integers $l$ and $r$ , which means that Mark will append letters $s_l s_{l+1} \ldots s_r$ to the end of string $s$ . Note that the length of $s$ increases after this operation.

Of course, Mark needs to be able to see what has been written. After copying, Mark will ask $q$ queries: given an integer $k$ , determine the $k$ -th letter of the final string $s$ .

The first line contains a single integer $t$ ( $1\leq t\leq 1000$ ) — the number of test cases.

The first line of each test case contains three integers $n$ , $c$ , and $q$ ( $1\leq n\leq 2\cdot 10^5$ , $1\leq c\leq 40$ , and $1\leq q\leq 10^4$ ) — the length of the initial string $s$ , the number of copy-pasting operations, and the number of queries, respectively.

The second line of each test case contains a single string $s$ of length $n$ . It is guaranteed that $s$ only contains lowercase English letters.

The following $c$ lines describe the copy-pasting operation. Each line contains two integers $l$ and $r$ ( $1\leq l\leq r\leq 10^{18}$ ). It is also guaranteed that $r$ does not exceed the current length of $s$ .

The last $q$ lines of each test case describe the queries. Each line contains a single integer $k$ ( $1\leq k\leq 10^{18}$ ). It is also guaranteed that $k$ does not exceed the final length of $s$ .

It is guaranteed that the sum of $n$ and $q$ across all test cases does not exceed $2\cdot 10^5$ and $10^4$ , respectively.

For each query, print the $k$ -th letter of the final string $s$ .

In the first test case, the copy-paste process is as follows.

• The first step is pasting string $\texttt{mark}$ at the end, yielding the string $\texttt{mark}\color{red}{\texttt{mark}}$ .
• The second step is pasting string $\texttt{mar}$ at the end, yielding the string $\texttt{markmark}\color{red}{\texttt{mar}}$ .
• The third step is pasting string $\texttt{rkmark}$ at the end, yielding the string $\texttt{markmarkmar}\color{red}{\texttt{rkmark}}$ .

In the second test case, the copy-paste process is as follows.

• The first step is pasting string $\texttt{re}$ at the end, yielding the string $\texttt{creamii}\color{red}{\texttt{re}}$ .
• The second step is pasting string $\texttt{ea}$ at the end, yielding the string $\texttt{creamiire}\color{red}{\texttt{ea}}$ .
• The third step is pasting string $\texttt{reamiire}$ at the end, yielding the string $\texttt{creamiireea}\color{red}{\texttt{reamiire}}$ .