ICPC North America Championship 2021

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2021-08-14 07:00 AKDT

ICPC North America Championship 2021

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2021-08-14 10:30 AKDT
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Problem G
Permutation CFG

Consider a permutation of the integers $1$ to $n$. Now, consider each number $1$ through $n$ to be a non-terminal in a Context-Free Grammar (CFG). Each number $k$ expands a list of the integers from $1$ to $k$ in the order of the permutation. For example, if $n=4$ and the permutation is $1$ $4$ $3$ $2$:

$1 \implies 1$

$2 \implies 1$ $2$

$3 \implies 1$ $3$ $2$

$4 \implies 1$ $4$ $3$ $2$

Now, consider a process of starting with $n$, and at each step, applying these rules to create a new list of integers. In the above example, at the first step:

$\overbrace{1 \; 4 \; 3 \; 2}^{4}$

At the second step:

$\overbrace{1}^{1} \overbrace{1 \; 4 \; 3 \; 2}^{4} \; \overbrace{1 \; 3 \; 2}^{3} \; \overbrace{1 \; 2}^{2}$

At the third step:

$ \overbrace{1}^{1} \overbrace{1}^{1} \overbrace{1 \; 4 \; 3 \; 2}^{4} \; \overbrace{1 \; 3 \; 2}^{3} \; \overbrace{1 \; 2}^{2} \overbrace{1}^{1} \overbrace{1 \; 3 \; 2}^{3} \; \overbrace{1 \; 2}^{2} \overbrace{1}^{1} \overbrace{1 \; 2}^{2}$

Given a permutation, a number of steps, and a list of queries asking for the number of occurrences of a particular integer in a prefix of the list created by the process, answer all of the queries.

Input

The first line of input contains three integers, $n$ ($2 \le n \le 10^5$), $s$ ($1 \le s \le 5 $) and $q$ ($1 \le q \le 2 \cdot 10^5$), where $n$ is the size of the permutation, $s$ is the number of steps to apply the process, and $q$ is the number of queries.

Each of the next $n$ lines contains a single integer $p$ ($1 \le p \le n$). This is the permutation, in order. All of the values of $p$ will be distinct.

Each of the next $q$ lines contains two integers $k$ ($1 \le k \le n$) and $a$ ($1 \le a \le 10^{9}$, $a$ will not exceed the length of the final list). This is a query for the number of occurrences of the integer $k$ in the first $a$ elements of the list created by the process.

Output

Output $q$ lines, each with a single integer, which are the answers to the queries in the order that they appear in the input.

Sample Input 1 Sample Output 1
4 3 6
1
4
3
2
1 6
2 20
4 1
3 5
2 9
1 16
3
6
0
1
2
8