408974: GYM103401 C Easy Nim

lyw and his friend zyw are playing an boring game called Easy Nim. In this game, there is a pile of $$$n$$$ stones on the table. Two players take turns choosing some stones and removing them from the table. The game always starts from lyw and ends when there is no stone left on the table. The player who removes the last stone wins this game.

But they all felt that the rules of the game were a bit boring, so they added some additional constraints. First, the player can only remove at least $$$1$$$ stone and at most $$$m$$$ stones from the table each round. The second, zyw will have $$$k$$$ extra magic cards as a blessing from God. Each card has a number written on it. When zyw uses this magic card, he can change the upper limit of the stone that can be removed in the rest round of the game to it, but he can't remove any stones during the round when he uses the magic card. Note that each card could be used only once.

Support that both of them are witty enough to win the Easy Nim game, please tell Jury who can win this game?

The input contain two lines.

The first line contains three intergers $$$n,\ m,\ k\ (1 \leq n \leq 1,000,000,000;\ 1 \leq m \leq 1,000,000;\ 1\leq k \leq 1,000)$$$ representing when the game start there are $$$n$$$ stones on the table and most $$$m$$$ stones can be removed in each round and zyw will have $$$k$$$ magic cards.

The second line contains $$$k$$$ intergers, the $$$i$$$-th interger $$$c_{i}\ (1 \leq c_{i} \leq 1,000,000)$$$ representing the number written on the $$$i$$$-th card.

Print lyw if lyw will win, otherwise zyw.

10 5 1
2

zyw

10 5 1
3

lyw