Problem Statement

The happiness of $a permutation P=(P_1,P_2,\ldots,P_N)$ of $(1,\dots,N)$ is defined as follows.

• Let $A=(A_1,A_2,\ldots,A_{N-1})$ be a sequence of length N-1 with $A_i = |P_i-P_{i+1}|(1\leq i \leq N-1)$. The happiness of P is the length of a longest strictly increasing subsequence of A.

Print a permutation P such that P_1 = X with the greatest happiness.

Input

Input is given from Standard Input in the following format:
N X

Output

Print a permutation P such that P_1 = X with the greatest happiness, in the following format:
$P_1 P_2 \ldots P_N$

If there are multiple solutions, printing any of them will be accepted.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $1 \leq X \leq N$
• All values in input are integers.

Sample Input 1

3 2

Sample Output 1

2 1 3

Since A=(1,2), the happiness of P is 2, which is the greatest happiness achievable, so the output meets the requirement.

Sample Input 2

3 1

Sample Output 2

1 2 3

Since A=(1,1), the happiness of P is 1, which is the greatest happiness achievable, so the output meets the requirement.

见题面 Input 部分

见题面 Output 部分