Score : $300$ points

Problem Statement

You are given an integer sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$.

Find the maximum value of $\displaystyle \sum_{i=1}^{M} i \times B_i$ for a contiguous subarray $B=(B_1,B_2,\dots,B_M)$ of $A$ of length $M$.

Notes

A contiguous subarray of a number sequence is a sequence that is obtained by removing $0$ or more initial terms and $0$ or more final terms from the original number sequence.

For example, $(2, 3)$ and $(1, 2, 3)$ are contiguous subarrays of $(1, 2, 3, 4)$, but $(1, 3)$ and $(3,2,1)$ are not contiguous subarrays of $(1, 2, 3, 4)$.

Constraints

• $1 \le M \le N \le 2 \times 10^5$
• $- 2 \times 10^5 \le A_i \le 2 \times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer.

4 2
5 4 -1 8

15

When $B=(A_3,A_4)$, we have $\displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times (-1) + 2 \times 8 = 15$. Since it is impossible to achieve $16$ or a larger value, the solution is $15$.

Note that you are not allowed to choose, for instance, $B=(A_1,A_4)$.

10 4
-3 1 -4 1 -5 9 -2 6 -5 3

31