A11590. Cashback

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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.

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 $a$ .

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

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.