Problem AA
SNim
Arthur and his sister Carol have been playing a game called Nim for some time now. Nim is played as follows:

The starting position has a number of heaps, all containing some, not necessarily equal, number of beads.

The players take turns chosing a heap and removing a positive number of beads from it.

The first player not able to make a move, loses.
Arthur and Carol really enjoyed playing this simple game until they recently learned an easy way to always be able to find the best move:

Xor the number of beads in the heaps in the current position (i.e., if we have $2$, $4$ and $7$ the xorsum will be $1$ since $2\ \mathbf{xor}\ 4\ \mathbf{xor}\ 7 = 1$).

If the xorsum is $0$, too bad, you will lose.

Otherwise, move such that the xorsum becomes $0$. This is always possible.
It is quite easy to convince oneself that this works. Consider these facts:

The player that takes the last bead wins.

After the winning player’s last move the xorsum will be $0$.

The xorsum will change after every move.
Which means that if you make sure that the xorsum always is $0$ when you have made your move, your opponent will never be able to win, and, thus, you will win.
Understandably it is no fun to play a game when both players know how to play perfectly (ignorance is bliss). Fortunately, Arthur and Carol soon came up with a similar game, $S$Nim, that seemed to solve this problem. Each player is now only allowed to remove a number of beads in some predefined set $S$, e.g. if we have $S = \{ 2, 5\} $ each player is only allowed to remove $2$ or $5$ beads. Now it is not always possible to make the xorsum $0$ and, thus, the strategy above is useless. Or is it?
Your job is to write a program that determines if a position of $S$Nim is a losing or a winning position. A position is a winning position if there is at least one move to a losing position. A position is a losing position if there are no moves to a losing position. This means, as expected, that a position with no legal moves is a losing position.
Input
The first line of input contains a number $k$ ($1 \le k \le 100$) describing the size of $S$, followed by $k$ numbers $s_ i$ ($1 \le s_ i \le 10\, 000$) describing $S$. The second line contains a number $m$ ($1 \le m \le 100$) describing the number of positions to evaluate. The next $m$ lines each contain a number $l$ ($1 \le l \le 100$) describing the number of heaps and $l$ numbers $h_ i$ ($0 \le h_ i \le 10\, 000$) describing the number of beads in the heaps.
Output
For each position:

If the described position is a winning position print a ‘W’.

If the described position is a losing position print an ‘L’.
Sample Input 1  Sample Output 1 

2 2 5 3 2 5 12 3 2 4 7 4 2 3 7 12 
LWW 
Sample Input 2  Sample Output 2 

5 1 2 3 4 5 3 2 5 12 3 2 4 7 4 2 3 7 12 
WWL 