9572: ABC242 —— D - ABC Transform
[Creator : ]
Description
You are given a string $S$ consisting of `A`, `B`, `C`.
Let $S^{(0)}:=S$. For $i=1,2,3,\ldots$, let $S^{(i)}$ be the result of simultaneously replacing the characters of $S^{(i-1)}$ as follows: `A` → `BC`, `B` → `CA`, `C` → `AB`.
Answer $Q$ queries. The $i$-th query is as follows.
- Print the $k_i$-th character from the beginning of $S^{(t_i)}$.
Let $S^{(0)}:=S$. For $i=1,2,3,\ldots$, let $S^{(i)}$ be the result of simultaneously replacing the characters of $S^{(i-1)}$ as follows: `A` → `BC`, `B` → `CA`, `C` → `AB`.
Answer $Q$ queries. The $i$-th query is as follows.
- Print the $k_i$-th character from the beginning of $S^{(t_i)}$.
Input
Input is given from Standard Input in the following format:
```
$S$
$Q$
$t_1$ $k_1$
$t_2$ $k_2$
$\hspace{0.4cm}\vdots$
$t_Q$ $k_Q$
```
```
$S$
$Q$
$t_1$ $k_1$
$t_2$ $k_2$
$\hspace{0.4cm}\vdots$
$t_Q$ $k_Q$
```
Output
Process the $Q$ queries in ascending order of index, that is, in the given order. Each answer should be followed by a newline.
Constraints
- $S$ is a string of length between $1$ and $10^5$ (inclusive) consisting of `A`, `B`, `C`.
- $1 \leq Q \leq 10^5$
- $0 \leq t_i \leq 10^{18}$
- $1 \leq k_i \leq \min(10^{18},$ the length of $S^{(t_i)})$
- $Q, t_i, k_i$ are integers.
- $1 \leq Q \leq 10^5$
- $0 \leq t_i \leq 10^{18}$
- $1 \leq k_i \leq \min(10^{18},$ the length of $S^{(t_i)})$
- $Q, t_i, k_i$ are integers.
Sample 1 Input
ABC
4
0 1
1 1
1 3
1 6
Sample 1 Output
A
B
C
B
We have $S^{(0)}$=ABC, $S^{(1)}$=BCCAAB.
Thus, the answers to the queries are A, B, C, B in the given order.
Sample 2 Input
CBBAACCCCC
5
57530144230160008 659279164847814847
29622990657296329 861239705300265164
509705228051901259 994708708957785197
176678501072691541 655134104344481648
827291290937314275 407121144297426665
Sample 2 Output
A
A
C
A
A