**Time limit:**1.00 s**Memory limit:**512 MB

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`