#P1754. TwinkleTwinkleLittleStar

TwinkleTwinkleLittleStar

Twinkle,twinkle, little star, how I wonder what you are.

Upabove the world so high, like a diamond in the sky.

Twinkle,twinkle, little star, how I wonder what you are.

Whenthe blazing sun is gone, when he nothing shines upon.

Theyou show your little light, Twinkle, twinkle, little star

Twinkle,twinkle, little star, How I wonder what you are.

Twinkle,twinkle, little star, how I wonder what you are.

----<Twinkle,twinkle, little star.>

 

Well, this songmay take us back to our childhood. When we were young, we often looked up atthe stars. How amazing they were! But, unfortunately, as we are becoming olderand older, what used to be interesting can not interest us now. So what we cando is to find something more interesting!

Here is one,maybe. Assume that all the stars are so far from us that we can treat them aspoints in a plane. You are given N stars in the plane, and a number K (0≤K≤N).What you need to do is to find the minimum square covering at least K stars,whose edges are all parallel to the axis. The stars which are on the edges ofthe square are also covered.

Input

The input will consist of multiple cases. Your program should process to the end of the input file.In the first line of one case, there are two integer N and K, 0<N≤1500, 0≤K≤N.
The next N lines are the description of the stars, one star per line. The ith line consists of two integers Xi and Yi, |Xi|<1000000, |Yi|<1000000.

Output

The output will consist of one line for each case, in the format of “Case X: Y”, while X is the case number counting from 1, and Y is the edge length of the minimum square. X and Y are all integers.

Sample Input

4 4
0 0
0 1
1 0
2 2
4 2
0 0
1 1
2 2
3 3

Sample Output

</p>
Case 1: 2
Case 2: 1

HINT

Huge input, scanf is recommended.

Source