Pivot Splitting (APCS 2018-02 Advanced)

2.0s 256M

Each entry is a positive weight at a unit-spaced position. Split an interval \([l,r]\) at an interior pivot \(p\) minimizing \(|\sum_{i=l}^r(i-p)a_i|\), choosing the leftmost on ties. Remove the pivot and recursively split both sides. The first split has depth \(1\); stop beyond depth \(K\) or with fewer than three entries. Sum the removed weights.

Input

Read \(n,K\), then the \(n\) weights.

Constraints

\(1\le n\le50000\), \(0\le K<30\), \(a_i\ge1\), \(\sum a_i\le10^9\).

Output

Print the sum of removed weights.

Sample Input 1

7 1
2 4 1 3 7 6 9

Sample Output 1

7

Sample Input 2

7 3
2 4 1 3 7 6 9

Sample Output 2

11

Source

f638 · 2018-02 APCS.

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