The widest road

There were two families in the village — family A and family B, while these two families didn’t get along well with each other. Now the head of the village decided to make a road through the village and it must be straight, for a straight line makes the way shortest and meanwhile, saves the cost. At that time, the heads of the two families proposed, because they didn’t want their own families live separated along the two sides of the road, thus it might decrease the solidarity of family. Besides, the two families were antipathetic to each other; neither wanted to live together with the other in a same side of the road. Then it made the village head in a pickle, he hoped the road to be as wide as possible. So what’s the possible maximal width of this road?
In order to simplify the problem, let’s regard the living place of each family member is just a point.

There are several test cases in the input.

The first line of each input contains n and m (1 ≤ m,n ≤ 1000). As for the following n lines, there are two numbers in every line, representing the living places of A family members. And the following m lines represent the living places of B family members.

The output numbers of each line are the maximal width of the road (retain four decimal), while if it’s impossible to make such a road, then just output 0.0000.

3 3
0.0 0.0
1.0 0.0
0.0 1.0
4.0 0.0
5.0 0.0
4.0 1.0

3.0000

2009 Multi-University Training Contest 1 - Host by TJU