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