Get the area

Time Limit: 1000MS

Memory Limit: 65535KB

Description

Weather in Nanjing, known as one of the four hottest stoves in China, is more and more intolerable recently. Especially for the sales promotion staff in summer, the only tool they can use is an old and shabby beach umbrella. There exists a small hole in the center of the umbrella.We can assume that the active area of the beach umbrella is an annulus. And the center is at the origin. The staff want to cover the tree shadow with the shabby beach umbrella .In this case, what they care most is the area of the tree shadow on the 3rd Road  in Nanjing University of Science & Technology they can take advantage of with the shabby beach umbrella.


Input

The first line contains three numbers: a positive double r1 (0 < r1 ≤ 1000.0) giving the radius of the umbrella; a positive double r2 (0 ≤ r2 ≤ r1) giving the radius of the small hole;and a positive integer m (3 ≤ m ≤ 50) giving the number of vertexes of the shadow. These are followed by m lines, each containing a vertex of the shadow.Two vertexes in adjacent lines are also adjacent on the shadow.


Output

Output the area of tree shadow they take advantage of with the umbrella.The error of answers in the range of 0.01 will be accepted.


Sample Input

10 0 3
0 20
10 0
-10 0
10 1 3
0 20
10 0
-10 0

Sample Output

144.35
142.78

Hint

None

Source

None

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