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Time Limit: 1.0 Seconds Memory Limit: 65536K

Total Runs: 1948 Accepted Runs: 515

Assume the coasting is an infinite straight line. Land is in one side of coasting,
sea in the other. Each small island is a point locating in the sea side. And any
radar installation, locating on the coasting, can only cover *d* distance, so an
island in the sea can be covered by a radius installation, if the distance between
them is at most *d*.

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

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