CF940E.Cashback

普及/提高-

通过率：0%

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题目描述

Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.

You are given an array $a$ of length $n$ and an integer $c$ .

The value of some array $b$ of length $k$ is the sum of its elements except for the smallest. For example, the value of the array $[3,1,6,5,2]$ with $c=2$ is $3+6+5=14$ .

Among all possible partitions of $a$ into contiguous subarrays output the smallest possible sum of the values of these subarrays.

输入格式

The first line contains integers $n$ and $c$ ( $1<=n,c<=100000$ ).

The second line contains $n$ integers $a_{i}$ ( $1<=a_{i}<=10^{9}$ ) — elements of $a$ .

输出格式

Output a single integer — the smallest possible sum of values of these subarrays of some partition of $a$ .

输入输出样例

输入#1
```
3 5
1 2 3
```
输出#1
```
6
```

输入#2

12 10
1 1 10 10 10 10 10 10 9 10 10 10

输出#2

输入#3
```
7 2
2 3 6 4 5 7 1
```
输出#3
```
17
```
输入#4
```
8 4
1 3 4 5 5 3 4 1
```
输出#4
```
23
```

说明/提示

In the first example any partition yields 6 as the sum.

In the second example one of the optimal partitions is $[1,1],[10,10,10,10,10,10,9,10,10,10]$ with the values 2 and 90 respectively.

In the third example one of the optimal partitions is $[2,3],[6,4,5,7],[1]$ with the values 3, 13 and 1 respectively.

In the fourth example one of the optimal partitions is $[1],[3,4,5,5,3,4],[1]$ with the values 1, 21 and 1 respectively.

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