CF578A.A Problem about Polyline

普及/提高-

通过率：0%

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题目描述

There is a polyline going through points $(0,0)–(x,x)–(2x,0)–(3x,x)–(4x,0)–...-(2kx,0)–(2kx+x,x)–...$ .

We know that the polyline passes through the point $(a,b)$ . Find minimum positive value $x$ such that it is true or determine that there is no such $x$ .

输入格式

Only one line containing two positive integers $a$ and $b$ ( $1<=a,b<=10^{9}$ ).

输出格式

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed $10^{-9}$ . If there is no such $x$ then output $-1$ as the answer.

输入输出样例

输入#1
```
3 1
```
输出#1
```
1.000000000000
```
输入#2
```
1 3
```
输出#2
```
-1
```
输入#3
```
4 1
```
输出#3
```
1.250000000000
```

说明/提示

You can see following graphs for sample 1 and sample 3.

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