A14576 | Divine Array

Black is gifted with a Divine array $a$ consisting of $n$ ( $1 \le n \le 2000$ ) integers. Each position in $a$ has an initial value. After shouting a curse over the array, it becomes angry and starts an unstoppable transformation.

The transformation consists of infinite steps. Array $a$ changes at the $i$ -th step in the following way: for every position $j$ , $a_j$ becomes equal to the number of occurrences of $a_j$ in $a$ before starting this step.

Here is an example to help you understand the process better:

Initial array: $2$ $1$ $1$ $4$ $3$ $1$ $2$ After the $1$ -st step: $2$ $3$ $3$ $1$ $1$ $3$ $2$ After the $2$ -nd step: $2$ $3$ $3$ $2$ $2$ $3$ $2$ After the $3$ -rd step: $4$ $3$ $3$ $4$ $4$ $3$ $4$ ......In the initial array, we had two $2$ -s, three $1$ -s, only one $4$ and only one $3$ , so after the first step, each element became equal to the number of its occurrences in the initial array: all twos changed to $2$ , all ones changed to $3$ , four changed to $1$ and three changed to $1$ .

The transformation steps continue forever.

You have to process $q$ queries: in each query, Black is curious to know the value of $a_x$ after the $k$ -th step of transformation.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 1000$ ). Description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1 \le n \le 2000$ ) — the size of the array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le n$ ) — the initial values of array $a$ .

The third line of each test case contains a single integer $q$ ( $1 \le q \le 100\,000$ ) — the number of queries.

Next $q$ lines contain the information about queries — one query per line. The $i$ -th line contains two integers $x_i$ and $k_i$ ( $1 \le x_i \le n$ ; $0 \le k_i \le 10^9$ ), meaning that Black is asking for the value of $a_{x_i}$ after the $k_i$ -th step of transformation. $k_i = 0$ means that Black is interested in values of the initial array.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2000$ and the sum of $q$ over all test cases doesn't exceed $100\,000$ .

For each test case, print $q$ answers. The $i$ -th of them should be the value of $a_{x_i}$ after the $k_i$ -th step of transformation. It can be shown that the answer to each query is unique.