Being a fan of contemporary architecture, Farmer John has built a new barn in the shape of a perfect circle. Inside, the barn consists of a ring of n rooms, numbered clockwise from 1…n around the perimeter of the barn (3≤n≤1,000). Each room has doors to its two neighboring rooms, and also a door opening to the exterior of the barn.
Farmer John wants exactly ri cows to end up in room i (1≤ri≤1,000,000). To herd the cows into the barn in an orderly fashion, he plans to unlock k exterior doors (1≤k≤7), allowing the cows to enter through only those doors. Each cow then walks clockwise through the rooms until she reaches a suitable destination. Farmer John wants to unlock the exterior doors that will cause his cows to collectively walk a minimum total amount of distance after entering the barn (they can initially line up however they like outside the k unlocked doors; this does not contribute to the total distance in question). Please determine the minimum total distance his cows will need to walk, if he chooses the best k such doors to unlock.

The first line of input contains n and k. Each of the remaining n lines contain r1…rn.

Please write out the minimum amount of distance the cows need to travel.

6 2
2
5
4
2
6
2

14

Farmer John can unlock doors 2 and 5. 11 cows enter at door 2 and walk a total distance of 8 to get to rooms 2, 3, and 4. 10 cows enter at door 5 and walk a total distance of 6 to get to rooms 5, 6 and 1.