I encounter the following optimization problem, but I can't solve it.

Given N variables satisfying $0 <= x_1 < x_2 < x_3 < ... < x_N <= 1$ and an integer K no large than N, find the values of $\{x_i\}$ that maximize the following function.

$$\sum_{S \subset \{1,2,..., N\}, |S| = K} \prod_{i≠j \in S} (x_i - x_j)^2.$$

This problem is somehow related to Vandermonde matrix. Each additional term in the above target function is just the square of the determinate of Vandermonde matrix generated by the K selected variables belonging set $S$.