Append Average

You are given an array $A$ of length $N$. You must perform the following operation **exactly** $K$ times: - Choose two distinct indices $i$ and $j$ ($1 \le i \lt j \leq N$). - Then, - If $(A_i + A_{j})$ is even, append $\frac{A_i + A_{j}}{2}$ to $A$. - If $(A_i + A_{j})$ is odd, append $\frac{A_i + A_{j} + 1}{2}$ to $A$. - $N$ is increased by $1$ after this. Find the minimum possible su