CF549E.Sasha Circle

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.

伯兰德人喜欢在辛苦工作一天后吃甜筒。米沙·斯夸尔（Misha Square）和萨沙·圆圈（Sasha Circle）是伯兰德当地的权威人物，各自掌控若干个甜筒销售点：米沙有 $n$ 个销售点，萨沙有 $m$ 个销售点。由于双方下属之间频繁发生冲突，他们决定修建一道圆形围栏，使得其中一位商人的所有销售点严格位于圆内，而另一位商人的所有销售点严格位于圆外。至于哪位商人的销售点位于圆内，这并不重要。

请判断他们能否修建这样一道围栏。

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 ( - 104 ≤ M__x, M__y ≤ 104), coordinates of Misha's trade points.

The next m lines contains pairs of space-separated integers S__x, S__y ( - 104 ≤ S__x, S__y ≤ 104), coordinates of Sasha's trade points.

It is guaranteed that all n + m points are distinct.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 10000$），分别表示米沙和萨沙的交易点数量。

接下来的 $n$ 行，每行包含一对用空格分隔的整数 $M_x,\ M_y$（$-10^4 \leq M_x, M_y \leq 10^4$），表示米沙的交易点坐标。

接下来的 $m$ 行，每行包含一对用空格分隔的整数 $S_x,\ S_y$（$-10^4 \leq S_x, S_y \leq 10^4$），表示萨沙的交易点坐标。

保证全部 $n + m$ 个点互不相同。

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.

唯一的一行输出应包含单词“YES”（不带引号），表示可以建造这样的围栏；否则，输出单词“NO”。

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.

在第一个样例中，无法将点分离，因为任何包含两点 $(-1, 0)$、$(1, 0)$ 的圆，也必定包含集合 $\{(0, -1), (0, 1)\}$ 中至少一个点；反之，任何包含两点 $(0, -1)$、$(0, 1)$ 的圆，也必定包含集合 $\{(-1, 0), (1, 0)\}$ 中至少一个点。

在第二个样例中，一种可能的解如下图所示。米沙的点用红色标记，萨沙的点用蓝色标记。