# [Usaco2005 jan]Naptime 午睡时间

时间限制：5s 空间限制：64MB

### 题目描述

Goneril is a very sleep-deprived cow. Her day is partitioned into N (3 <= N <= 3,830) equal time periods but she can spend only B (2 <= B < N) not necessarily contiguous periods in bed. Due to her bovine hormone levels, each period has its own utility U_i (0 <= U_i <= 200,000), which is the amount of rest derived from sleeping during that period. These utility values are fixed and are independent of what Goneril chooses to do, including when she decides to be in bed. With the help of her alarm clock, she can choose exactly which periods to spend in bed and which periods to spend doing more critical items such as writing papers or watching baseball. However, she can only get in or out of bed on the boundaries of a period. She wants to choose her sleeping periods to maximize the sum of the utilities over the periods during which she is in bed. Unfortunately, every time she climbs in bed, she has to spend the first period falling asleep and gets no sleep utility from that period. The periods wrap around in a circle; if Goneril spends both periods N and 1 in bed, then she does get sleep utility out of period 1. What is the maximum total sleep utility Goneril can achieve?

### 输入格式

* Line 1: Two space-separated integers: N and B

* Lines 2..N+1: Line i+1 contains a single integer, U_i, between 0 and 200,000 inclusive

### 输出格式

* Line 1: A single integer, the maximum total sleep utility Goneril can achieve.

### 样例输入

5 3 2 0 3 1 4

### 样例输出

6 选择时间段1（入睡），4，2

### 提示

见国家队2005 Twb,ZgL作业

### 题目来源

Gold