You are given a string $S$ consisting of uppercase and lowercase English letters.

We perform the following operation on $S$ $10^{100}$ times:

-   First, create a string $T$ by changing uppercase letters in $S$ to lowercase, and lowercase letters to uppercase.
-   Then, concatenate $S$ and $T$ in this order to form a new $S$.

Answer $Q$ queries. The $i$-th query is as follows:

-   Find the $K_i$-th character from the beginning of $S$ after all operations are completed.

The input is given from Standard Input in the following format:

```
$S$
$Q$
$K_1$ $K_2$ $\dots$ $K_Q$
```

Let $C_i$ be the answer to the $i$-th query. Print them in a single line, separated by spaces, in the following format:

```
$C_1$ $C_2$ $\dots$ $C_Q$
```

-   $S$ is a string consisting of uppercase and lowercase English letters, with length between $1$ and $2 \times 10^5$, inclusive.
-   $Q$ and $K_i$ are integers.
-   $1 \le Q \le 2 \times 10^5$
-   $1 \le K_i \le 10^{18}$

a B A b A b a B A b a B a B A b

Before the operations, $S = $ `aB`.

-   After performing the operation once on `aB`, it becomes `aBAb`.
-   After performing the operation twice on `aB`, it becomes `aBAbAbaB`.
-   $\dots$

After performing the operation $10^{100}$ times, $S = $ `aBAbAbaBAbaBaBAb`...