Maximize Product

You are given two integers $N$ and $K$. Consider all ways to represent $N$ as the sum of exactly $K$ distinct positive integers $x_1, x_2, \dots, x_K$ — in other words, $x_i \gt 0$ for each valid $i$, $x_i \neq x_j$ for each valid $i \neq j$ and $x_1 + x_2 + \ldots + x_K = N$ should hold. You have to find the maximum possible value of the product $(x_1^2 - x_1) \cdot (x_2^2 - x_2) \cdot \ldots \c