Consider a game where two players remove sticks from a heap. The players move alternately, and the player who removes the last stick wins the game.
A set $P={p_1,p_2,\ldots,p_k}$ determines the allowed moves. For example, if $P={1,3,4}$ , a player may remove $1$ , $3$ or $4$ sticks.
Your task is find out for each number of sticks $1,2,\dots,n$ if the first player has a winning or losing position.
The first input line has two integers $n$ and $k$ : the number of sticks and moves.
The next line has $k$ integers $p_1,p_2,\dots,p_k$ that describe the allowed moves. All integers are distinct, and one of them is $1$ .
Print a string containing $n$ characters: W means a winning position, and L means a losing position.