Imagine a board with n pins put into it, the i-th pin is located at (x_i, y_i). For simplicity, we will restrict the problem to the case where the pins are placed in vertices of a convex polygon.

Then, take a non-stretchable string of length l, and put it around all the pins. Place a pencil inside the string and draw a curve around the pins, trying to pull the string in every possible direction. The picture below shows an example of a string tied around the pins and pulled by a pencil (a point P).

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Your task is to find an area inside this curve. Formally, for a given convex polygon S and a length l let's define a fiber shape F(S, l) as a set of points t such that the perimeter of the convex hull of S ∪ \\{t\} does not exceed l. Find an area of F(S, l).

Input

The first line contains two integers n and l (3 ≤ n ≤ 10^4; 1 ≤ l ≤ 8 ⋅ 10^5) — the number of vertices of the polygon S and the length of the string. Next n lines contain integers x_i and y_i (-10^5 ≤ x_i, y_i ≤ 10^5) — coordinates of polygon's vertices in counterclockwise order. All internal angles of the polygon are strictly less than π. The length l exceeds the perimeter of the polygon by at least 10^{-3}.

Output

Output a single floating-point number — the area of the fiber shape F(S, l). Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}. 

Examples

Input


3 4
0 0
1 0
0 1


Output


3.012712585980357


Input


4 5
0 0
1 0
1 1
0 1


Output


5.682061989789656


Input


5 17
0 0
2 -1
3 0
4 3
-1 4


Output


37.719371276930820

Note

The following pictures illustrate the example tests.

<image> <image>

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Source: codeforces | Difficulty: VERY_HARD


Solutions: