154_E. Martian Colony_28604
The first ship with the Earth settlers landed on Mars. The colonists managed to build n necessary structures on the surface of the planet (which can be regarded as a plane, and the construction can be regarded as points on it). But one day the scanners recorded suspicious activity on the outskirts of the colony. It was decided to use the protective force field generating system to protect the colony against possible trouble.

The system works as follows: the surface contains a number of generators of the field (they can also be considered as points). The active range of each generator is a circle of radius r centered at the location of the generator (the boundary of the circle is also included in the range). After the system is activated, it stretches the protective force field only over the part of the surface, which is within the area of all generators' activity. That is, the protected part is the intersection of the generators' active ranges.

The number of generators available to the colonists is not limited, but the system of field generation consumes a lot of energy. More precisely, the energy consumption does not depend on the number of generators, but it is directly proportional to the area, which is protected by the field. Also, it is necessary that all the existing buildings are located within the protected area.

Determine the smallest possible area of the protected part of the surface containing all the buildings.

Input

The first line contains two integers n and r (1 ≤ n ≤ 105, 1 ≤ r ≤ 50000) — the number of buildings and the active ranges of the generators, correspondingly.

Next n lines contains the buildings' coordinates. The i + 1-th (1 ≤ i ≤ n) line contains two real numbers with at most three digits after the decimal point xi and yi (|xi|, |yi| ≤ 50000) — coordinates of the i-th building. It is guaranteed that no two buildings are located at the same point, and no two different buildings are located closer than 1.

It is guaranteed that there exists a circle with radius r that contains all the buildings.

Output

Print the single real number — the minimum area of the protected part containing all the buildings. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.

Examples

Input

3 5
0.00 0.000
0.0 8.00
6 8.00


Output

78.5398163397


Input

4 1000
0.0 0.0
0 2.00
2.00 2
2.0 0.00


Output

4.0026666140


Input

4 5
3.00 0.0
-3 0.00
0.000 1
0.0 -1.00


Output

8.1750554397

Note

In the first sample the given radius equals the radius of the circle circumscribed around the given points. That's why the circle that corresponds to it is the sought area. The answer is 25π.

In the second sample the area nearly coincides with the square which has vertexes in the given points.

The area for the third sample is shown on the picture below.

<image>
#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
  Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
  Point operator*(double k) const { return Point(x * k, y * k); }
  Point operator/(double k) const { return Point(x / k, y / k); }
};
struct Vertex {
  int id, lid, rid;
  double r;
  bool operator<(const Vertex &v) const {
    return r > v.r + EPS || (r > v.r - EPS && id < v.id);
  }
};
const int MAXN = 100 * 1000 + 5;
Point pol[MAXN], ch[MAXN];
Vertex v[MAXN];
char del[MAXN];
set<Vertex> st;
double sp(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }
double cp(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; }
double len(const Point &p) { return sqrt(sp(p, p)); }
bool operator<(const Point &a, const Point &b) {
  double cpp = cp(a - pol[0], b - pol[0]);
  return cpp > EPS || (cpp > -EPS &&
                       sp(a - pol[0], a - pol[0]) < sp(b - pol[0], b - pol[0]));
}
double getR(const Point &a, const Point &b, const Point &c) {
  return len(b - a) * len(c - b) * len(a - c) / (2 * fabs(cp(b - a, c - a)));
}
double getAngle(const Point &a, const Point &b) {
  return atan2(cp(a, b), sp(a, b));
}
double get2SegmentS(const Point &a, const Point &b, double r) {
  Point h = (a + b) / 2;
  double hlen = sqrt(r * r - sp(h - a, h - a));
  Point d = h - a;
  swap(d.x, d.y);
  d.x *= -1;
  d = d / len(d) * hlen;
  Point o = h + d;
  return (fabs(getAngle(a - o, b - o)) * r * r - fabs(cp(a - o, b - o)));
}
int buildCH(int n) {
  for (int i = 1; i < n; i++)
    if (pol[i].x < pol[0].x - EPS ||
        (pol[i].x < pol[0].x + EPS && pol[i].y < pol[0].y - EPS))
      swap(pol[i], pol[0]);
  if (n == 1) return 1;
  sort(pol + 1, pol + n);
  ch[0] = pol[0];
  ch[1] = pol[1];
  int h = 2;
  for (int i = 2; i < n; i++) {
    while (h >= 2 && cp(ch[h - 1] - ch[h - 2], pol[i] - ch[h - 1]) < EPS) h--;
    ch[h] = pol[i];
    h++;
  }
  while (h > 2 && cp(ch[h - 1] - ch[h - 2], pol[0] - ch[h - 1]) < EPS) h--;
  for (int i = 0; i < h; i++) pol[i] = ch[i];
  return h;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.setf(ios::fixed);
  cout.precision(10);
  int n, r;
  cin >> n >> r;
  for (int i = 0; i < n; i++) cin >> pol[i].x >> pol[i].y;
  n = buildCH(n);
  rotate(pol, pol + 1, pol + n);
  for (int i = 0; i < n; i++) {
    v[i].id = i;
    v[i].lid = (i == 0 ? n - 1 : i - 1);
    v[i].rid = (i == n - 1 ? 0 : i + 1);
    if (n > 2) v[i].r = getR(pol[i], pol[v[i].lid], pol[v[i].rid]);
  }
  for (int i = 0; i < n; i++) st.insert(v[i]);
  while (st.size() > 3 && st.begin()->r > r + EPS) {
    Vertex p = *st.begin();
    st.erase(st.begin());
    st.erase(v[p.lid]);
    st.erase(v[p.rid]);
    del[p.id] = true;
    v[p.lid].rid = p.rid;
    v[p.rid].lid = p.lid;
    v[p.lid].r = getR(pol[p.lid], pol[v[p.lid].lid], pol[v[p.lid].rid]);
    v[p.rid].r = getR(pol[p.rid], pol[v[p.rid].lid], pol[v[p.rid].rid]);
    st.insert(v[p.lid]);
    st.insert(v[p.rid]);
  }
  if (st.size() == 3 && st.begin()->r > r + EPS)
    for (set<Vertex>::iterator it = st.begin(); it != st.end(); it++)
      if (sp(pol[it->lid] - pol[it->id], pol[it->rid] - pol[it->id]) < EPS) {
        del[it->id] = true;
        st.erase(it);
        break;
      }
  if (st.size() == 1) {
    cout << 0 << '\n';
    return 0;
  }
  double s = 0;
  int fst = -1, lst = -1;
  for (int i = 0; i < n; i++)
    if (!del[i]) {
      if (fst == -1) fst = i;
      if (lst != -1) {
        s += cp(pol[lst], pol[i]);
        s += get2SegmentS(pol[lst], pol[i], r);
      }
      lst = i;
    }
  s += cp(pol[lst], pol[fst]);
  s += get2SegmentS(pol[lst], pol[fst], r);
  s /= 2;
  cout << s << '\n';
  return 0;
}

4 1000
0.0 0.0
0 2.00
2.00 2
2.0 0.00
 3 5
0.00 0.000
0.0 8.00
6 8.00
 4 5
3.00 0.0
-3 0.00
0.000 1
0.0 -1.00
 5 5
0 2
-1 -1
1 1
0 -1
2 0
 10 20
-5.871 -18.070
5.871 18.070
-19.000 0.000
-15.371 -11.167
15.371 11.167
5.871 -18.070
-15.371 11.167
15.371 -11.167
19.000 0.000
-5.871 18.070
 20 39
-19.871 -33.871
-26.118 19.193
2.590 32.924
11.371 -36.110
30.138 21.003
-23.960 -23.218
-2.715 -38.855
-31.374 16.522
23.116 -20.438
-16.028 33.617
18.090 -30.698
-22.225 -26.474
3.376 33.641
-33.681 -15.997
34.140 -1.904
-33.322 -7.109
-17.438 33.396
37.443 8.532
10.589 -33.069
-30.427 22.987
 9 3
1 2
-1 -2
1 -1
1 -2
-2 -2
2 1
-2 2
1 1
0 2
 5 200
0 200
6.279 199.605
6.279 -199.605
-6.279 199.605
0 -200
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 47
-1 6
-42 28
46 31
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -6
-17 45
-22 -26
7 35
30 -29
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 2 1
0 0
0 2
 10 20
15.371 11.167
-5.871 -18.070
-15.371 -11.167
-19.000 0.000
5.871 -18.070
-15.371 11.167
15.371 -11.167
19.000 0.000
5.871 18.070
-5.871 18.070
 3 5
0 0
0 8
6 8
 1 1
0 0
 20 40
-37.091 12.051
12.051 37.091
-12.051 -37.091
37.091 -12.051
-39.000 0.000
-12.051 37.091
-22.923 31.551
12.051 -37.091
22.923 -31.551
-31.551 -22.923
0.000 -39.000
22.923 31.551
31.551 22.923
39.000 0.000
-37.091 -12.051
-31.551 22.923
0.000 39.000
-22.923 -31.551
37.091 12.051
31.551 -22.923
 15 30
19.404 21.551
-3.031 -28.841
-28.366 6.029
26.492 11.795
-14.500 -25.114
29.000 0.000
26.492 -11.795
-23.461 -17.045
8.961 -27.580
-14.499 25.114
-28.366 -6.029
8.961 27.580
-3.031 28.841
19.404 -21.551
-23.461 17.045
 5 5
0 2
-1 -1
1 1
0 -1
3 0
 20 39
-19.871 -33.871
-26.118 19.193
2.590 32.924
11.371 -36.110
30.138 21.003
-23.960 -23.218
-2.715 -38.855
-31.374 16.522
23.116 -20.438
-16.028 33.617
18.090 -30.698
-22.225 -26.474
3.376 33.641
-33.681 -15.997
34.140 -1.904
-33.322 -7.085050559694364
-17.438 33.396
37.443 8.532
10.589 -33.069
-30.427 22.987
 9 3
1 2
-1 -2
1 -1
1 -3
-2 -2
2 1
-2 2
1 1
0 2
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 47
-1 6
-42 28
46 31
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -6
-17 45
-22 -26
7 35
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 10 20
15.371 11.167
-5.0207329669219805 -18.070
-15.371 -11.167
-19.000 0.000
5.871 -18.070
-15.371 11.167
15.371 -11.167
19.000 0.000
5.871 18.070
-5.871 18.070
 1 2
0 0
 4 5
3.00 0.0
-3 0.00
0.000 1
0.0 -0.26163709223105125
 5 5
0 2
-1 -2
1 1
0 -1
3 0
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 51
-1 6
-42 28
46 31
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -6
-17 45
-22 -26
7 35
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -6
-17 45
-22 -26
7 35
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 5 5
0 2
-1 -2
1 1
-1 -1
3 -1
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 28
46 58
-45 31
21 30
-27 -6
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
39 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 53
46 58
-45 31
21 30
-27 -6
-31 29
-28 -27
-7 29
18 2
-50 -3
-17 45
-22 -26
7 43
39 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 53
46 58
-45 31
21 30
-49 -6
-31 29
-28 -27
-7 29
18 2
-50 -3
-17 45
-22 -26
7 43
39 -4
-1 29
-35 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
39 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 53
46 58
-45 31
21 30
-49 -6
-31 29
-28 -27
-7 29
18 2
-50 -3
-17 45
-22 -26
7 43
39 -4
-1 29
-35 -13
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 46
 30 100
19 -24
39 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
46 58
-45 31
21 30
-49 -10
-31 29
-28 -27
-7 29
18 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -44
-26 46
 30 100
19 -24
39 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
46 77
-45 31
21 30
-49 -10
-31 29
-28 -27
-7 29
18 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -44
-26 46
 30 100
18 -24
39 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
37 77
-45 31
21 30
-49 -10
-31 29
-28 -27
-7 29
18 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -44
-26 46
 30 100
18 -24
14 -18
80 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
37 77
-45 31
21 30
-1 -10
-31 29
-28 -27
-7 29
18 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -44
-26 46
 30 100
18 -24
14 -18
80 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
37 121
-45 31
21 30
-1 -10
-31 29
-28 -27
-7 29
18 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -44
-26 46
 30 100
18 -28
14 -18
80 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 56
37 121
-45 31
21 30
-1 -10
-31 29
-28 -27
-7 29
26 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -25
-26 46
 30 100
18 -28
14 -18
80 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 110
37 121
-45 57
21 30
-1 -10
-9 29
-28 -27
-7 29
26 2
-50 -3
-19 45
-22 -26
7 43
39 -4
0 29
-35 -13
18 36
-2 -43
-34 24
-4 -24
21 -25
-26 46
 5 5
0 2
-1 -1
0 1
0 -1
2 0
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 47
-1 6
-42 28
46 31
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -6
-17 44
-22 -26
7 35
30 -29
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 3 5
0 0
0 8
6 1
 20 40
-37.091 12.051
12.051 37.091
-12.051 -36.46786657195662
37.091 -12.051
-39.000 0.000
-12.051 37.091
-22.923 31.551
12.051 -37.091
22.923 -31.551
-31.551 -22.923
0.000 -39.000
22.923 31.551
31.551 22.923
39.000 0.000
-37.091 -12.051
-31.551 22.923
0.000 39.000
-22.923 -31.551
37.091 12.051
31.551 -22.923
 4 1001
0.0 0.0
0 2.00
2.00 2
2.0 0.00
 5 5
0 2
-1 -2
1 1
-1 -1
1 0
 5 5
0 2
-1 0
1 1
-1 -1
3 -1
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-60 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 9 3
1 2
-1 -2
1 -1
1 -3
-2 -2
2 1
-2 2
1 1
-1 2
 5 5
0 2
-1 -2
1 1
-1 -1
3 0
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 35
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-40 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-47 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -8
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -6
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
30 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 28
46 40
-45 31
21 30
-27 -6
-31 29
-28 -27
-7 39
18 2
-50 -3
-17 45
-22 -26
7 30
39 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
-8 19
-57 -15
-33 -42
-3 51
-1 6
-42 28
46 58
-45 31
21 30
-27 -6
-31 29
-28 -27
-7 29
18 2
-50 -3
-17 45
-22 -26
7 30
39 -4
-1 29
-50 -43
18 36
-2 -24
-18 24
-4 -24
21 -44
-26 24
 30 100
19 -24
40 -18
45 27
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