## Description

In the land of our great Sultan, the World Weird Fence (WWF) festival is going to take place again. For the festival, some poles are set up in a Cartesian plane. Each pole is colored in either red or blue color. You can connect two poles with a chain that consists of multi-colored rings thus creating a weird fence. Each pole has a single hook so you can not connect more than one chain to a pole. Now, though you have an unlimited supply of chains all having the same length, it¡¯s important to note that each of the chains has a red ring at one end & a blue ring at the other end and you are only allowed to hook up a ring to a pole with same color. Also, it¡¯s obvious that you can use a chain to connect two poles if & only if the chain¡¯s length is greater than or equal to the linear distance of those two poles. Given the co-ordinates of the poles & a positive integer k, write a program to find the minimum possible integer length for the chains so that at least k weird fences can be made. The fences may cross each other.## Input

The first line of the input file is the number of test cases N. This line will be followed by a blank line. N test cases follow. First line of each test case contains two positive integers P & k where P is the number of poles on the plane. (1<=P,k<=100). Each of the next P lines has two integers X & Y & the word ¡°red¡± / ¡°blue¡±. X & Y are the co-ordinates of the pole (-1000<=X,Y<=1000) & the word is the color of that pole. No two poles will be in the same location. There will be a blank line between test cases.## Output

For each test case output a single integer in a line which is the minimum integer length of the chains that is necessary to make at least k fences. If it is not possible to build k fences with the given constraints, print the word ¡°Impossible¡± in a single line.## Sample Input

2 6 2 -3 5 blue -3 3 red 1 5 blue 2 0 red 4 6 blue 4 -1 red 6 4 -3 5 blue -3 3 red 1 5 blue 2 0 red 4 6 blue 4 -1 red## Sample Output

6 Impossible## Source

Sultan's Contest