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This round has an unusual addition to the rules. For each problem you must use distinct language. Thus, if you have a submission that has passed at least one test or is being tested at the moment, then for this task you can use only this language and can not use it for other tasks. More details can be read by the link. Different implementations of the same language are considered to be the same language (for example, in C++ you can only solve one problem, regardless of the exact chosen compiler).

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G. Perfectionist Arkadiy

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputArkadiy has lots square photos with size *a* × *a*. He wants to put some of them on a rectangular wall with size *h* × *w*.

The photos which Arkadiy will put on the wall must form a rectangular grid and the distances between neighboring vertically and horizontally photos and also the distances between outside rows and columns of photos to the nearest bound of the wall must be equal to *x*, where *x* is some non-negative real number. Look on the picture below for better understanding of the statement.

Arkadiy haven't chosen yet how many photos he would put on the wall, however, he want to put at least one photo. Your task is to determine the minimum value of *x* which can be obtained after putting photos, or report that there is no way to put positive number of photos and satisfy all the constraints. Suppose that Arkadiy has enough photos to make any valid arrangement according to the constraints.

Note that Arkadiy wants to put at least one photo on the wall. The photos should not overlap, should completely lie inside the wall bounds and should have sides parallel to the wall sides.

Input

The first line contains three integers *a*, *h* and *w* (1 ≤ *a*, *h*, *w* ≤ 10^{9}) — the size of photos and the height and the width of the wall.

Output

Print one non-negative real number — the minimum value of *x* which can be obtained after putting the photos on the wall. The absolute or the relative error of the answer must not exceed 10^{ - 6}.

Print -1 if there is no way to put positive number of photos and satisfy the constraints.

Examples

Input

2 18 13

Output

0.5

Input

4 4 4

Output

0

Input

3 4 3

Output

-1

Note

In the first example Arkadiy can put 7 rows of photos with 5 photos in each row, so the minimum value of *x* equals to 0.5.

In the second example Arkadiy can put only 1 photo which will take the whole wall, so the minimum value of *x* equals to 0.

In the third example there is no way to put positive number of photos and satisfy the constraints described in the statement, so the answer is -1.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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