Sasha Circle

题意翻译

- $n+m$ 个整点。 - 询问是否存在一个圆将前 $n$ 个点和后 $m$ 个点严格分开。 - $n,|x|,|y| \le 10^4$。

题目描述

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.

输入输出格式

输入格式

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 $ M_{x},M_{y} $ ( $ -10^{4}<=M_{x},M_{y}<=10^{4} $ ), coordinates of Misha's trade points. The next $ m $ lines contains pairs of space-separated integers $ S_{x},S_{y} $ ( $ -10^{4}<=S_{x},S_{y}<=10^{4} $ ), coordinates of Sasha's trade points. It is guaranteed that all $ n+m $ points are distinct.

输出格式

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.

输入输出样例

输入样例 #1

2 2
-1 0
1 0
0 -1
0 1

输出样例 #1

NO

输入样例 #2

4 4
1 0
0 1
-1 0
0 -1
1 1
-1 1
-1 -1
1 -1

输出样例 #2

YES

说明

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.