Chef Odd

You want to partition the set $S = \{1, 2, \ldots, N\}$ into $K$ sets $S_1, S_2, \ldots, S_K$, such that $|S_i| \ge 2$, and the sum of elements in each $S_i$ is odd. Is it possible to do so? **Note 1:** Partitioning the set $S = \{1, 2, \ldots, N\}$ into $K$ sets $S_1, S_2, \ldots, S_K$ means that every element of $S$ should be in exactly one of the sets $S_1, S_2, \ldots, S_K$, and $S_i \subset