We use Cartesian coordinate system, defining the coasting is the x-axis. The
sea side is above x-axis, and the land side below. Given the position of each
island in the sea, and given the distance of the coverage of the radar installation,
your task is to write a program to find the minimal number of radar installations
to cover all the islands. Note that the position of an island is represented
by its x-y coordinates.

**Input**

The input consists of several test cases. The first line of each case contains
two integers n (1 <= n <= 1000) and d, where n is the number of islands in the sea
and d is the distance of coverage of the radar installation. This is followed
by n lines each containing two integers representing the coordinate of the position
of each island. Then a blank line follows to separate the cases.

The input is terminated by a line containing pair of zeros.

**Output**

For each test case output one line consisting of the test case number followed by the minimal number of radar installations needed. "-1" installation means no solution for that case.

**Sample Input**

3 2

1 2

-3 1

2 1

1 2

0 2

0 0

Sample Output

Case 1: 2

Case 2: 1