A11976 | Shashlik Cooking

Long story short, shashlik is Miroslav's favorite food. Shashlik is prepared on several skewers simultaneously. There are two states for each skewer: initial and turned over.

This time Miroslav laid out $n$ skewers parallel to each other, and enumerated them with consecutive integers from $1$ to $n$ in order from left to right. For better cooking, he puts them quite close to each other, so when he turns skewer number $i$ , it leads to turning $k$ closest skewers from each side of the skewer $i$ , that is, skewers number $i - k$ , $i - k + 1$ , ..., $i - 1$ , $i + 1$ , ..., $i + k - 1$ , $i + k$ (if they exist).

For example, let $n = 6$ and $k = 1$ . When Miroslav turns skewer number $3$ , then skewers with numbers $2$ , $3$ , and $4$ will come up turned over. If after that he turns skewer number $1$ , then skewers number $1$ , $3$ , and $4$ will be turned over, while skewer number $2$ will be in the initial position (because it is turned again).

As we said before, the art of cooking requires perfect timing, so Miroslav wants to turn over all $n$ skewers with the minimal possible number of actions. For example, for the above example $n = 6$ and $k = 1$ , two turnings are sufficient: he can turn over skewers number $2$ and $5$ .

Help Miroslav turn over all $n$ skewers.

The first line contains two integers $n$ and $k$ ( $1 \leq n \leq 1000$ , $0 \leq k \leq 1000$ ) — the number of skewers and the number of skewers from each side that are turned in one step.

The first line should contain integer $l$ — the minimum number of actions needed by Miroslav to turn over all $n$ skewers. After than print $l$ integers from $1$ to $n$ denoting the number of the skewer that is to be turned over at the corresponding step.