Minimum of sum of six squares over a polytope

Question

$$\begin{array}{ll} \text{minimize} & x_1^2 + x_2^2 + \cdots + x_6^2\\ \text{subject to} & x_1 + x_2 + \cdots + x_6 = K\\ & x_1 + x_2 \ge k_1\\ & x_1 + x_2 + x_3 + x_4 \ge k_2\\ & x_1 \ge x_2 \ge x_3 \ge x_4 \ge x_5 \ge x_6 \ge 0\end{array}$$