Uva10859 - Placing Lampposts

As a part of the mission `Beauti cation of Dhaka City', the government has decided to replace all the

old lampposts with new expensive ones. Since the new ones are quite expensive and the budget is not

up to the requirement, the government has decided to buy the minimum number of lampposts required

to light the whole city.

Dhaka city can be modeled as an undirected graph with no cycles, multi-edges or loops. There are

several roads and junctions. A lamppost can only be placed on junctions. These lampposts can emit

light in all the directions, and that means a lamppost that is placed in a junction will light all the roads

leading away from it.

The `Dhaka City Corporation' has given you the road map of Dhaka city. You are hired to nd

the minimum number of lampposts that will be required to light the whole city. These lampposts can

then be placed on the required junctions to provide the service. There could be many combinations of

placing these lampposts that will cover all the roads. In that case, you have to place them in such a

way that the number of roads receiving light from two lampposts is maximized.

Input

There will be several cases in the input le. The rst line of input will contain an integer T (T  30)

that will determine the number of test cases. Each case will start with two integers N (N  1000)

and M (M < N) that will indicate the number of junctions and roads respectively. The junctions are

numbered from 0 to N