CZ-SK-MO 1992 Problem 1

For a permutation $p(a_1,a_2,...,a_{17})$ of $1,2,...,17$ , let $k_p$ denote the largest $k$ for which $a_1 +...+a_k < a_{k+1} +...+a_{17}$ . Find the maximum and minimum values of $k_p$ and find the sum $\sum_{p} k_p$ over all permutations $p$ .