Divine Array
Description
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.
Input
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 $100\,000$.
Output
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.
Samples
2
7
2 1 1 4 3 1 2
4
3 0
1 1
2 2
6 1
2
1 1
2
1 0
2 1000000000
1
2
3
3
1
2
Note
The first test case was described ih the statement. It can be seen that:
- $k_1 = 0$ (initial array): $a_3 = 1$;
- $k_2 = 1$ (after the $1$-st step): $a_1 = 2$;
- $k_3 = 2$ (after the $2$-nd step): $a_2 = 3$;
- $k_4 = 1$ (after the $1$-st step): $a_6 = 3$.
For the second test case,
| Initial array: | $1$ $1$ |
| After the $1$-st step: | $2$ $2$ |
| After the $2$-nd step: | $2$ $2$ |
| ... | ... |
It can be seen that:
- $k_1 = 0$ (initial array): $a_1 = 1$;
- $k_2 = 1000000000$: $a_2 = 2$;