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.

Input

The first input line has two integers $n$ and $k$: the number of sticks and moves.

The next line has $k$ integers $p_1,p_2,\dots,p_k$ 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

• $1 \le n \le 10^6$
• $1 \le k \le 100$
• $1 \le p_i \le n$

Example

Input:

10 3
1 3 4

Output:

WLWWWWLWLW