Score : $400$ points

Problem Statement

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 $S^{(t_i)}$.

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.

Input

Input is given from Standard Input in the following format:

$S$

$Q$

$t_1$ $k_1$

$t_2$ $k_2$

$\hspace{0.4cm}\vdots$

$t_Q$ $k_Q$

Output

Process the $Q$ queries in ascending order of index, that is, in the given order. Each answer should be followed by a newline.

ABC
4
0 1
1 1
1 3
1 6

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.

CBBAACCCCC
5
57530144230160008 659279164847814847
29622990657296329 861239705300265164
509705228051901259 994708708957785197
176678501072691541 655134104344481648
827291290937314275 407121144297426665

A
A
C
A
A