2398: Sasha Circle
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
Berlanders like to eat cones after a hard day. Misha Square and Sasha Circle are local authorities of Berland. Each of them controls its points of cone trade. Misha has n points, Sasha − m. Since their subordinates constantly had conflicts with each other, they decided to build a fence in the form of a circle, so that the points of trade of one businessman are strictly inside a circle, and points of the other one are strictly outside. It doesn't matter which of the two gentlemen will have his trade points inside the circle.
Determine whether they can build a fence or not.
The first line contains two integers n and m (1≤n,m≤10000), numbers of Misha's and Sasha's trade points respectively.
The next n lines contains pairs of space-separated integers Mx,My (-104≤Mx,My≤104), coordinates of Misha's trade points.
The next m lines contains pairs of space-separated integers Sx,Sy (-104≤Sx,Sy≤104), coordinates of Sasha's trade points.
It is guaranteed that all n+m points are distinct.
The only output line should contain either word "YES" without quotes in case it is possible to build a such fence or word "NO" in the other case.
2 2
-1 0
1 0
0 -1
0 1
NO
4 4
1 0
0 1
-1 0
0 -1
1 1
-1 1
-1 -1
1 -1
YES
In the first sample there is no possibility to separate points, because any circle that contains both points (-1,0),(1,0) also contains at least one point from the set (0,-1),(0,1), and vice-versa: any circle that contains both points (0,-1),(0,1) also contains at least one point from the set (-1,0),(1,0)
In the second sample one of the possible solution is shown below. Misha's points are marked with red colour and Sasha's are marked with blue. 