You are the owner of a restaurant, and you are serving for N customers seating in a round table.
You will distribute M menus to them. Each customer receiving a menu will make the order of plates, and then pass the menu to the customer on the right unless he or she has not make the order. The customer i takes Li unit time for the ordering.
Your job is to write a program to calculate the minimum time until all customers to call their orders, so you can improve your business performance.
The input consists of a sequence of positive integers.
The first line of the input contains two positive integers N (N ≤ 50,000) and M (M ≤ N). The second line contains N positive integers L1, L2,..., LN (Li ≤ 600).
Output the minimum possible time required for them to finish ordering.
3 2 1 5 10
4 2 1 2 3 4