K-Subarrays Solution Codechef -You are given two integers NN and KK, and an array AA of NN integers. You have to choose KK disjoint non-empty subarrays such that the score is maximized.

  

K-Subarrays Solution Codechef -  

SOLUTION

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You are given two integers N$N$ and K$K$, and an array A$A$ of N$N$ integers. You have to choose K$K$ disjoint non-empty subarrays such that the score is maximized.

The score is calculated as follows:

Score=∑i=1KSum[i]⋅i,$$\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}=\sum _{i=1}^K\mathrm{S}\mathrm{u}\mathrm{m}[i]\cdot i,$$

where Sum[i]$\mathrm{S}\mathrm{u}\mathrm{m}[i]$ denotes sum of elements of i$i$-th subarray. By the i$i$-th subarray, we mean the i$i$-th one in the order from left to right.

Find the maximum score that can be achieved.

Note: The subarrays are not required to cover the whole array. It is allowed for some elements of A$A$ to belong to none of the subarrays.

Input

• The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
• The first line of each test case contains two space-separated integers N$N$ and K$K$.
• The second line of each test case contains N$N$ space-separated integers A1,A2,…,AN$A_1,A_2,\dots ,A_N$.

Output

For each test case, print a single line containing one integer ― the maximum score.

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤K≤min(100,N)$1\le K\le min(100,N)$
• −106≤Ai≤106$-{10}^6\le A_i\le {10}^6$
• The sum of N$N$ over all test cases does not exceed 105${10}^5$

Subtasks

• Subtask #1 (15 points): K=1$K=1$
• Subtask #2 (35 points): K=2$K=2$
• Subtask #3 (50 points): Original constraints

Sample Input

2
5 2
1 2 -1 3 1
5 2
-1 2 11 -23 12

Sample Output

11
37

Explanation

• Test Case 1: One way to choose 2$2$ disjoint non-empty subarrays is:

S1=[1,2]$S_1=[1,2]$ and S2=[3,1]$S_2=[3,1]$

The score is 3⋅1+4⋅2=11$3\cdot 1+4\cdot 2=11$, which is the maximum possible.

• Test Case 2: One way to choose 2$2$ disjoint non-empty subarrays is:

S1=[2,11]$S_1=[2,11]$ and S2=[12]$S_2=[12]$

The score is 13⋅1+12⋅2=37$13\cdot 1+12\cdot 2=37$, which is the maximum possible.

Date Added:29-05-2021

Time Limit:1 secs

Source Limit:50000 Bytes

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SOLUTION

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