All Tracks Data Structures Stacks Basics of Stacks Problem

Monk Celebrating Checkpoint
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Data Structures, Medium, Stack, approved

Problem
Editorial
Analytics

Monk is feeling happy to reach the first checkpoint in his journey. in order to have fun, he asked Mishki to solve a problem for him.

She will be given an array of $$N$$ distinct elements, and needs to perform at most $$X$$ arbitrary operations. In each operation she can select any element from the array and can increase it by exactly $$1$$. She can perform at max $$1$$ operation over any element of the array.

The special thing about this array is that, for any $$2$$ elements $$( A [ i ] , A [ j ] )$$, where $$( i ≠ j )$$, $$a b s ( A [ i ] − A [ j ] ) \ge K$$, where $$abs(x)$$ denotes the absolute value of any integer $$x$$.

Now, we define $$3$$ functions :

$$F ( i , j )$$: = $$Max(i,j) - Min(i,j)$$

$$Max(i,j)$$ = Maximum element present in the sub array ranging from $$i , i + 1... j $$ in array $$A$$.

$$ Min(i,j)$$ = Minimum element present in the sub array ranging from $$i , i + 1.. j$$ in array $$A $$.

Mishki needs to perform exactly $$X$$ operations, and then needs to tell Monk the following :

$$answer$$ = $$\sum_{i=1}^{N} \sum_{j=i}^{N} F(i,j)$$

In short, she needs to tell Monk the summation of the difference between the maximum and minimum element of each sub array of array $$A$$ . Considering Mishki performs the $$X$$ operations given to her optimally what is the maximum value of answer that she can achieve ?

Help Mishki for the same.

Input Format :

The first line will consists of $$3$$ space separated integers $$N$$, $$X$$ and $$K$$ , denoting the number of elements in the array, operations needs to be performed and minimum absolute difference between any $$2$$ elements of the array respectively.
In next line, there will be $$N$$ space separated integers, $$A [ i ]$$ , where $$1 \le i \le N$$, denoting the elements of array.

Output Format

Print the required maximum possible maximum value of answer.

Constraints: :

$$2 \le N \le 10^5$$

$$1 \le X \le N$$

$$1 \le A [ i ] \le 10^6$$

$$ 2 \le K \le 10$$

SAMPLE INPUT
3 1 2
2 4 6
SAMPLE OUTPUT
10
Explanation

Here, N= 4, X =1 and K =2

So, if we increase last element, i.e 6 by 1, the required sum will become 10.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

CodeMonk (Checkpoint - I)

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