Problem Statement

You and Grant have played many times a game that extends the so-called "Don't Say $21$ Game" (also known in some places as the stick-taking game) using positive integers $N,K$. The rules are as follows.

1. First, the first player is given $0$.
2. From there, while avoiding declaring a number that is $N$ or greater (declaring one means losing), the player declares the given number plus any integer from $1〜K$ and passes it to the opponent.
3. The players alternate repeating step 2. until the game is decided.

Since you have learned how to win this game, Grant has become unable to win it.
So Grant decided to challenge you with the following rule added.

4. Some "dangerous numbers" between $1$ and $N-1$, inclusive, are specified. Declaring a "dangerous number" means losing.

You start the game as the first player.
Here, assuming that both players move so as not to lose, and given natural numbers $N,K$,
if you can win, output all the numbers you can declare first in order to win, separated by newlines. If you cannot win, output $0$.

Input

$N\ K$
$S$

$N, K$ are integers
$1 \le K < N \le 2\times 10^5$
$S$ is a string of length $N-1$ consisting of o or x
If the $i$-th character of $S$ is x, then $i$ is a "dangerous number"

Output

If you can win, output all the numbers you can declare first in order to win, separated by newlines. If you cannot win, output $0$ followed by a newline.

Sample

21 3
oooooooooooooooooooo

0

21 3
oooxoooxoooxoooxooox

3

50 5
ooxoooxxoxoooxooooxxxoxxooxoxoxooooxxooxooooxoooo

2