A+B

Two strings $P = P_1 P_2 \cdots P_n$ and $Q = Q_1 Q_2 \cdots Q_n$ of the same length $n$ are called orthogonal if $P_i \ne Q_i$ for every $i$ with $1 \le i \le n$. A string $S$ of length $n$ is orthogonal to a set of strings $V = {V_1, V_2, \ldots, V_m}$ (each also of length $n$) if $S$ is orthogonal to $V_j$ for every $j$ with $1 \le j \le m$.

Fix the alphabet of lowercase English letters. Given a set $V$, take all strings of length $n$ that are orthogonal to $V$ and sort them in ascending lexicographic order. This yields a sequence $T = T_0, T_1, \ldots, T_{M-1}$, where $M$ is the number of such strings.

The orthogonal sum of $A = T_a$ and $B = T_b$ is the string $C = T_c$ where $c = (a + b) \bmod M$.

Given the set $V$ and two strings $A$ and $B$ (both orthogonal to $V$), compute the orthogonal sum $C$ of $A$ and $B$ with respect to $V$.

The first line contains two integers $n$ and $k$: the length of each string $n$ ($1 \le n \le 100000$) and the number of strings in $V$, with $1 \le n \cdot k \le 100000$. Each of the next $k$ lines contains one string $V_j$. The following two lines contain the strings $A$ and $B$, each of length $n$.

All strings $V_j$, $A$, and $B$ consist of lowercase English letters. It is guaranteed that $A$ and $B$ are orthogonal to $V$.

Print the orthogonal sum $C$ of $A$ and $B$ with respect to $V$.