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.