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#3964

Circular Barn 2s 512MB

Problems

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 \ldots n around the perimeter of the barn (3 \leq n \leq 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 r_i cows to end up in room i (1 \leq r_i \leq 1,000,000). To herd the cows into the barn in an orderly fashion, he plans to unlock k exterior doors (1 \leq k \leq 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.

Problem credits: Brian Dean


Input

The first line of input contains n and k. Each of the remaining n lines contain r_1 \ldots r_n.


Output

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


Example 

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.


Source

USACO 2016 February Platinum

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