Index × A(Not Continuous ver.)

AtCoder

IDabc267_d

Time2000ms

Memory256MB

Difficulty—

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 (not necessarily contiguous) subsequence $B=(B_1,B_2,\dots,B_M)$ of length $M$ of $A$. ## Constraints * $1 \le M \le N \le 2000$ * $- 2 \times 10^5 \le A_i \le 2 \times 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ [samples] ## Notes A **subsequence** of a number sequence is a sequence that is obtained by removing $0$ or more elements from the original number sequence and concatenating the remaining elements without changing the order. For example, $(10,30)$ is a subsequence of $(10,20,30)$, but $(20,10)$ is not a subsequence of $(10,20,30)$.

Samples

Input #1

4 2
5 4 -1 8

Output #1

21

When $B=(A_1,A_4)$, we have $\displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times 5 + 2 \times 8 = 21$. Since it is impossible to achieve $22$ or a larger value, the solution is $21$.

Input #2

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

Output #2

API Response (JSON)

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