Problem Description

In 2046, no more people can be held in our planet-earth. Fortunately, with the development of science and technology, human find the 10th planet of solar system, named Flirly, in honor of a great physicist Flirly. Observation and analysis show us that the condition and resource in the planet is comfortable to our living. So, more and more people immigrate to it. Reality, however, is not as perfect as people imagine. Actually, enormous Aliens live in this planet and they feel being disturbed by the human's immigration, therefore launch severe wars against us again and again. Although human being hope to have close emotional attach with the Aliens, they only have to resort to the durable war strategy and passive defense against the enemy's attacks, due to their unfamiliarity with the geological condition of the planet.

One day, people escape to a great plain, amazed by many stones arising from the ground. For this, people find a method, which is to build thick walls along these stones, to resist the attack. For simplicity, we suppose that each wall between two stones is linearly built. And certainly, these walls are close and form a layer against Alien's attack. However, considering that the more layers Aliens's destruct ,the more energy is consumed, only one layer is not enough and people have to build as many layers as possible. Of course any two of these layers can intersect and one stone merely belongs to one layer. With protection of such condition-fit walls, people can gather in the center closed by these walls. In order to acommodate more people, the area of the center is as large as possible.

In case being attacked by the Aliens immediately, human beings have to build these stone-wall defense system in short time. Before this, they have to know the max time of the Aliens destruct these condition-fit walls(we postulate that time consumed in a close wall is a constant).Under this precondition, they also have to know the max area of the center closed by these walls.

Input

The first line of input file contains an integer T which implies the total test cases in it.
For each test case, it contains:

Line 1: Two space-separated integers: N, K (3<=N<=1000,1<=k<=100000)which specify the total number of stones and time Aliens destruct a layer of walls.
Line 2..N+1: Two space-separated integers, Xi and Yi (-100000 <=Xi, Yi <= 100000) specifying the coordinates of a stone's position. Among the set of all stones locations, no two points are the same and no three points are collinear.

Output

For each case,ouput format is as following:

Line 1: a string which is "Case id:". Case id will started from 1.
Line 2: Two number:T,K which secify the total time Aliens consume in destructing all the layers and the area of the center closed by these walls. T is an interger and K is a real number which is accurate to three fractional digits.The two numbers are seperated by a blank space.

Print a blank line between test cases.

Sample Input

3
4 1
-1 -1
1 -1
1 1
-1 1
5 1
-2 -2
2 -2
2 2
-2 2
0 1
8 3
-1 -1
1 -1
1 1
-1 1
5 0
-5 0
0 5
0 -5

Sample Output

Case 1:
1 4.00

Case 2:
1 16.00

Case 3:
6 4.00

Hint

This figure shows the first sample above

From: WHUCPC'2005