7750: [CSES Problem Set] Stick Game
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Description
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 $P=\{p_1,p_2,…,p_k\}$ 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 $1,2,…,n$ if the first player has a winning or losing position.
A set $P=\{p_1,p_2,…,p_k\}$ determines the allowed moves. For example, if $P=\{1,3,4\}$, a pla
Your task is find out for each number of sticks $1,2,…,n$ if the first pla
Input
The first input line has two integers $n$ and $k$: the number of sticks and moves.
The next line has $k$ integers $p_1,p_2,…,p_k$ that describe the allowed moves. All integers are distinct, and one of them is $1$.
The next line has $k$ integers $p_1,p_2,…,p_k$ that describe the allowed moves. All integers are distinct, and one of them is $1$.
Output
Print a string containing $n$ characters: $W$ means a winning position, and $L$ means a losing position.
Constraints
$1≤n≤10^6$
$1≤k≤100$
$1≤p_i≤n$
$1≤k≤100$
$1≤p_i≤n$
Sample 1 Input
10 3
1 3 4
Sample 1 Output
WLWWWWLWLW