Problem Statement

You are given $K$ strings $S_1, S_2, \ldots, S_K$ consisting of a and b. Also, for an integer $i > K$, define the string $S_i$ as the concatenation of $S_{i-1}, S_{i-2}, \ldots, S_{i-K}$ in this order.

You perform the following operation on a string $T$.

• Perform the following operations for $j = 1, 2, \ldots, |S_N|$ in order, where $|S_N|$ is the length of $S_N$.
• If the $j$-th character of $S_N$ is a, move the first character of $T$ to the end.
  • If the $j$-th character of $S_N$ is b, reverse $T$ entirely. That is, reverse the order of the characters of $T$.

Find the string $T$ after the series of operations.

Constraints

• $2 \leq K \leq 100$
• $K$ is an integer.
• $S_i$ is a non-empty string consisting of a and b. $(1 \leq i \leq K)$
• The sum of the lengths of $S_1, S_2, \ldots, S_K$ is at most $2 \times 10^5$.
• $1 \leq N \leq 10^{18}$
• $N$ is an integer.
• $T$ is a string consisting of lowercase English letters with length between $1$ and $2 \times 10^5$, inclusive.

Input

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

K
S_1
S_2
\vdots
S_K
N
T

Output

Output the answer.