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.

Sample Input 1

4 2
5 4 -1 8

Sample Output 1

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, $B=(A_1,A_4)$.

Sample Input 2

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

Sample Output 2

31