Kyriakos Grizzly wants to create a new workout routine over the course of the next ~N~ days. In order for a workout routine to be good, the amount of weights he lifts each day must be pairwise distinct, and must be in the range ~[1,10^9]~. Furthermore, the sum of the weights over the ~N~ days must be divisible by ~K~ for maximal gains. Can you create a good workout routine for Kyriakos, or let him know that it's impossible?

Constraints

~1 \le N, K \le 10^6~

Subtask 1 [20%]

~1 \le N \times K \le 10^9~

Subtask 2 [80%]

No additional constraints.

Input Specification

The only line of input contains 2 integers ~N~ and ~K~.

Output Specification

If no good workout routine exists output ~-1~.

Otherwise, output one line containing ~N~ integers. The integers must all be distinct and must all be in the range ~[1,10^9]~, and their sum must be divisible by ~K~.

Sample Input

6 9

Sample Output

2 5 7 3 10 9