http://codeforces.com/contest/1206/problem/C

I found a challenge in the editorial (http://codeforces.com/blog/entry/69158) :

Challenge:

For which pairs of (n,k) (n>k≥1) is there an arrangement of numbers from 1 to n on a circle such that the sums of each k consecutive numbers differ by not more than 1 ? ( The problem above is a specify case where n=2*k)

My solution is: - if k is even, there are no n satisfied the condition. - if k is odd, only n=2*k satisfied the condition.

Can someone verify this for me?

Thank you very much.