We need to calculate how many times each number from the input appears as the largest of ~K~ numbers in every combination. If we sort the numbers in ascending order, we can see that this number is going to be maximal in an array of ~K~ numbers if all other numbers are located to its left. Therefore, the ~i^\text{th}~ number is maximal the exact number of times as the number of ways to choose ~K-1~ numbers out of the first ~i~ numbers. If we denote the number of ways to choose ~K~ numbers out of ~N~ numbers as ~f(n, k)~, then it is easy to see that ~f(n, k) = f(n-1, k)+f(n-1, k-1)~.

Using this relation, we can calculate each ~f(n, k)~.

The solution is therefore the sum of the product of the corresponding ~f(i, k-1)~ and ~v[i]~, where ~v[i]~ is the value on that location.