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)}.

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.

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.

Sample Input 1

ABC
4
0 1
1 1
1 3
1 6

Sample Output 1

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 Input 2

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

Sample Output 2

A
A
C
A
A

见题面 Input 部分

见题面 Output 部分