Given a string $S$, $n$ strings $T_1,T_2,\ \dots,\ T_n$ of length $m$ and a positive rational number sequence $p$ of length $k$ whose sum is $1$. Each string consists of only the first $k$ lowercase letters. Let's perform the following procedure:

1. If there exists $j\ (1 \leq j \leq n)$ such that $T_j$ is a substring of $S$, stop the procedure.
2. Append the $i$-th lowercase letter with probability $p_i$ to the end of $S$, then return to step 1.

Let's define $f(S;T,p)$ as the expected length of $S$ when the procedure stops.
It's boring to calculate $f(S;T,p)$ for only one string $S$. To make the problem much harder, a string $R$ is given. Let's denote the prefix of $R$ of length $i$ as $R[1 \dots i]$. Your task is to calculate $f(R[1 \dots i];T,p)$ for $i=1,\ 2,\ \cdots,\ |R|$.
It can be proved that $f(S;T,p)$ is a positive rational number and it can be represented as $\frac {P}{Q}$ with $\gcd(P,Q)=1$. It is guaranteed that $Q\not\equiv 0\ \text (mod \ {(10^9+7)})$ for all strings $S$ under the given $T$ and $p$ in the input. You should print the value of $PQ^{-1} \mod (10^9+7)$.

The first line contains three positive integers $n,\ m$ and $k\ (1 \leq n \leq 100,\ n \times m \leq 10,000,\ 1 \leq k \leq 26)$.
The second line contains $k$ positive integers $p'_1,\ p'_2\, \cdots,\ p'_k$. It is guaranteed that $p'_1+p'_2+\cdots+p'_k=100$ and the probability $p_i$ equals to $\frac{p'_i}{100}$.
The $i$-th line of the following $n$ lines contains a string $T_i$ of length $m$.
The last line contains a string $R\ (1 \leq |R| \leq 10,000)$.
It is guaranteed each string consists of only the first $k$ lowercase letters and $Q \not\equiv 0 \pmod{(10^9+7)}$ when representing $f(S;T,p)$ as $\frac {P}{Q}$ with $\gcd(P,Q)=1$ for all strings $S$ under the given $T$ and $p$ in the input.

Ouput $|R|$ lines. The $i$-th line contains an integer representing the value of $f(R[1 \dots i];T,p)$.