Problem H
Ograda

Matija needs to paint his old fence. The fence is made from $N$ planks, each $1$ cm in width and varying in height. To do this easy and fast, he bought himself a Super Paint Roller Deluxe. The paint roller is $X$ cm wide. The Super Paint Roller Deluxe model comes with a catch, however. Matija must at all times touch the planks with full width of the roller, otherwise paint drops all around and stains everything. Also, the roller must always be parallel to the ground to prevent leakage. This means that in order for Matija to use the roller safely, he needs to select $X$ planks, and paint them from bottom to the top of the lowest plank in one swoop. Then he selects some other $X$ planks, paints them and so on.

This leaves parts of some planks unpainted. Matija will have to paint such parts with a toothbrush. This is obviously quite tedious so he asked you to help him paint as much as possible using the Super Paint Roller Deluxe. Since there is more than one way to do this he is also interested in the painting that requires the minimal number of swoops.

In the example of Figure 1 Matija needs two swoops with his roller – one to paint planks $1$, $2$ and $3$ to the height of $3\ \mathrm{cm}$, the other to paint planks $3$, $4$ and $5$ to the height of $4\ \mathrm{cm}$. Note that $3\ \mathrm{cm}^2$ ($2\ \mathrm{cm}^2$ on plank $1$ and $1\ \mathrm{cm}^2$ on plank $5$) are left unpainted. Also, $3\ \mathrm{cm}^2$ on plank $3$ are painted over twice, but that’s OK.

Figure 1: Sample 1

Input

The first line of input contains two integers $N$ ($1 \leq N \leq 1\, 000\, 000$), the number of planks, and $X$ ($1 \leq X \leq 100\, 000$), the width of the Super Paint Roller. The width of the Super Paint Roller will not exceed the width of the fence.

The second line of input contains $N$ positive integers, smaller than $1\, 000\, 000$, the heights of planks in the fence.

Output

The first line of output should contain the smallest possible area Matija will have to paint manually.

The second line of output should contain the smallest number of swoops needed.

5 3
5 3 4 4 5

3
2

10 3
3 3 3 3 3 3 3 3 3 3

0
4

7 4
1 2 3 4 3 2 1

4
4