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. Figure 1: A Sample Input of Radar Installation 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 32 12 -3 1 21 12 02
2/2 00 Sample Output Case 1: 2 Case 2: 1