SOLVE

LATER

Monk Celebrating Checkpoint

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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:** :

\(2 \le N \le 10^5\)

\(1 \le X \le N\)

\(1 \le A [ i ] \le 10^6\)

\( 2 \le K \le 10\)

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

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