Night has fallen, and ~N~ alpacas have gathered around a campfire. They sit in a circle, that is, alpaca ~1~ is to the right of alpaca ~N~, alpaca ~2~ is to the right of alpaca ~1~, alpaca ~3~ is to the right of alpaca ~2~, and so on. Each alpaca is waiting to be assigned a happiness index, ~h_i~. The ~i^\text{th}~ alpaca is happy if the sum of its happiness index and the happiness index of the alpaca to its right is even. Otherwise, it is sad. Being a diligent herdsman, you decide to assign each of the ~N~ alpacas a happiness index such that there are exactly ~X~ happy alpacas.

Constraints

~2 \le N \le 10^6~

~0 \le X \le N~

Subtask 1 [15%]

~2 \le N \le 15~

Subtask 2 [85%]

No additional constraints.

Input Specification

The first line contains two space-separated integers, ~N~ and ~X~.

Output Specification

If no solution exists, output ~-1~. Otherwise, output ~N~ space-separated integers, the happiness index ~h_i~ for the ~i^{th}~ alpaca ~(0 \le h_i \le 10^9)~. If there are multiple solutions, output any.

Note: Output must end with a newline with no trailing whitespace.

Sample Input 1

6 4

Sample Output 1

7 27 196 50 3 17

Explanation for Sample Output 1

The happy alpacas in this arrangement are alpaca ~1~, alpaca ~3~, alpaca ~5~, and alpaca ~6~. Note that this is not the only solution.

Sample Input 2

2 1

Sample Output 2

-1