ABSum

problem

Given a sequence $A$ of length $N$. You can swap the $i$ th and $j$ th ($0 \ leq i, j \ leq N-1$) elements of a sequence up to $M$ times.

Find the maximum value of $\ sum_ {i = 0} ^ {N -1} abs (A_i --i)$ in the sequence created by the operation.

output

Find the maximum value of $\ sum_ {i = 0} ^ {N --1} abs (A_i --i)$ in the sequence created by the operation. Also, output a line feed at the end.

Example

Input

5 2 0 3 2 1 4

Output

12

inputFormat

outputFormat

output

Find the maximum value of $\ sum_ {i = 0} ^ {N --1} abs (A_i --i)$ in the sequence created by the operation. Also, output a line feed at the end.

Example

Input

5 2 0 3 2 1 4

Output

12

样例

5 2
0 3 2 1 4

12