Problem D. Dragon claw ≡

• problems
 Author: G. Grenkin Time limit: 1 sec Input file: input.txt Memory limit: 256 Mb Output file: output.txt

Statement

A sculpture of dragon is established in the campus of Far Eastern Federal University. There are long claws on dragon's paws. According to a legend, when a student passes the session successfully, the claws grow a little (by several nanometers). That's why students took an interest how much the area of the claw will increase when the claw grows by d mm.

Students constructed the following mathematical model of dragon's claw growth. The claw has the shape of a convex polygon with a base on the abscissa axis. The claw grows equally in all directions and doesn't grow below its base. When the claw grows by d mm, all its sides shift in parallel by d mm to the outside (see the figure). The base of the claw remains at the same place, so one should intersect the new polygon with the abscissa axis.

Your program must calculate the area of the claw before and after its growing.

Input file format

Input file contains integers N d, followed by N pairs of integers xi yi — coordinates of vertices of the polygon in millimeters in the clockwise order. The polygon is non-degenerate.

Output file format

Output file must contain 2 real numbers: the area of the claw before and after growing in mm2 with at least 4 correct digits after the decimal point.

Constraints

3 ≤ N ≤ 40; 1 ≤ d ≤ 100;  − 100 ≤ xi ≤ 100; 0 ≤ yi ≤ 100; y1 = yn = 0.

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
5 2
-4 0
-6 1
-4 8
1 4
3 0
42.0000 89.9943
2
4 1
2 0
2 2
4 2
4 0
4.0000 12.0000

0.115s 0.020s 15