CF744D.Hongcow Draws a Circle

Hongcow really likes the color red. Hongcow doesn't like the color blue.

Hongcow is standing in an infinite field where there are n red points and m blue points.

Hongcow wants to draw a circle in the field such that this circle contains at least one red point, and no blue points. Points that line exactly on the boundary of the circle can be counted as either inside or outside.

Compute the radius of the largest circle that satisfies this condition. If this circle can have arbitrarily large size, print  - 1. Otherwise, your answer will be accepted if it has relative or absolute error at most 10 - 4.

红牛（Hongcow）非常喜欢红色，不喜欢蓝色。

红牛站在一个无限大的平面上，平面上有 $n$ 个红点和 $m$ 个蓝点。

红牛想在这个平面上画一个圆，使得该圆至少包含一个红点，且不包含任何蓝点。恰好落在圆边界上的点，可被视作在圆内或圆外（即边界点的归属可自由选择）。

请计算满足上述条件的最大可能圆的半径。若这样的圆可以任意大，请输出 -1；否则，你的答案只要满足相对误差或绝对误差不超过 $10^{-4}$ 即可被接受。

The first line of the input will contain two integers n, m (1 ≤ n, m ≤ 1, 000).

The next n lines will contain two integers x__i, y__i (1 ≤ x__i, y__i ≤ 104). This denotes the coordinates of a red point.

The next m lines will contain two integers x__i, y__i (1 ≤ x__i, y__i ≤ 104). This denotes the coordinates of a blue point.

No two points will have the same coordinates.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 1{,}000$）。

接下来的 $n$ 行，每行包含两个整数 $x_i$、$y_i$（$1 \leq x_i, y_i \leq 10^4$），表示一个红点的坐标。

再接下来的 $m$ 行，每行包含两个整数 $x_i$、$y_i$（$1 \leq x_i, y_i \leq 10^4$），表示一个蓝点的坐标。

任意两个点的坐标均不相同。

Print  - 1 if the circle can have arbitrary size. Otherwise, print a floating point number representing the largest radius circle that satisfies the conditions. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 4.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if .

如果圆的半径可以为任意大小，则输出 $-1$；否则，输出一个浮点数，表示满足条件的最大半径。当你的答案的绝对误差或相对误差不超过 $10^{-4}$ 时，即视为正确。

也就是说，假设你的答案为 $a$，评测组的答案为 $b$，则当满足 时，评测程序将判定你的答案正确。

This is a picture of the first sample

This is a picture of the second sample

这是第一个样例的图片

这是第二个样例的图片