Stick Game

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