Xiaohetao is organizing a premium walnut gift box. He arranges walnuts numbered $1 \sim n$ in a row, with corresponding positions also numbered $1 \sim n$. The final arrangement forms a permutation $p$ of $1 \sim n$, where $p_i$ represents the walnut number placed at the $i$-th position.

To measure the aesthetic value of the gift box, Xiaohetao defines the value score of a single walnut as: $$\min(|p_i - i|, m)$$ where $p_i$ represents the number of the walnut at the $i$-th position, and $m$ is a given constant.

That is, the score is the minimum of the distance between the walnut's actual position and its number, and the constant $m$. Xiaohetao wishes to maximize the total value score of all walnuts. Please construct any one permutation $p$ that satisfies this condition.

Input

A single line containing two integers $n$ and $m$, where $1 \le n \le 1000000$ and $1 \le m \le n$.

Output

Output a single line of integers representing the permutation you constructed.

Examples

Input 1

5 2

Output 1

3 4 5 1 2