2301: A Problem about Polyline
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputThere 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.
Examples
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.
