Index × A(Continuous ver.)

AtCoder

IDabc267_c

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 contiguous subarray $B=(B_1,B_2,\dots,B_M)$ of $A$ of length $M$. ## 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: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ [samples] ## 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 $(1, 2, 3, 4)$.

Samples

Input #1

4 2
5 4 -1 8

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, $B=(A_1,A_4)$.

Input #2

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

Output #2

API Response (JSON)

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    "name": "Index × A(Continuous ver.)",
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      "content": "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 $A$ ",
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    "sign": "abc267_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.\nFind 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 $A$ ...",
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