cf C. A Problem about Polyline （数学题）

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.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

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.

Sample test(s)

input

3 1

output

1.000000000000

input

1 3

output

-1

input

4 1

output

1.250000000000

Note

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

#include<iostream>#include<cstdio>#include<cmath>using namespace std;int main(){double a,b,l1,l2,ans2,ans1;cin>>a>>b;if(a<b) {printf("-1\n");return 0;}if(a==b) {printf("%.12lf\n",b);return 0;}l1=(a-b)/2;l2=(a+b)/2;double num1=floor(l1/b);double num2=floor(l2/b);ans1=l1/num1;ans2=l2/num2;if(ans1>ans2) printf("%.12lf\n",ans2);else printf("%.12lf\n",ans1);return 0;}