Show that the problem has unique KKT points for maximization problem $\max c_1x_1 + ... + c_nx_n$

Question

Consider the following maximization problem: $$\max \; c_1x_1 + ... + c_nx_n$$ subject to the constraints $$x_1^2 + ... + x_n^2 \leq 1 $$ $$x_1, .... , x_n \geq 0$$ where $c_1,...,c_n$ are constants such that at least one of them is positive (a) Show that the problem has a unique KKT point $x^*$ and find an explicit formula for it that expresses the coordinates $x_i^*$ in terms of the constants $c_1,...,c_n$