SOLVE
LATER
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: :
\(2 \le N \le 10^5\)
\(1 \le X \le N\)
\(1 \le A [ i ] \le 10^6\)
\( 2 \le K \le 10\)
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.