K Odd Sum

Given integers $N$ and $K$, construct a permutation $P = [P_1, P_2, \ldots, P_N]$ of the integers $\{1,2,\ldots, N\}$ such that there are **exactly** $K$ indices $i$ ($1 \le i \lt N$) for which $(P_i + P_{i + 1})$ is odd. It can be proved that the answer always exists under the constraint of $1 \le K \le N - 1$. If multiple answers exist, any of them will be accepted. **Note:** A permutation