Problem: 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>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template <typename T>
inline T max(T a, T b) {
  return a > b ? a : b;
}
template <typename T>
inline T min(T a, T b) {
  return a < b ? a : b;
}
template <typename T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
template <typename T>
inline bool repr(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <typename T>
inline bool repl(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline T gcd(T a, T b) {
  T t;
  if (a < b) {
    while (a) {
      t = a;
      a = b % a;
      b = t;
    }
    return b;
  } else {
    while (b) {
      t = b;
      b = a % b;
      a = t;
    }
    return a;
  }
}
template <typename T>
inline T sqr(T x) {
  return x * x;
}
struct Cg {
  __attribute__((always_inline)) inline char operator()() { return getchar(); }
};
struct Cp {
  __attribute__((always_inline)) inline void operator()(char x) { putchar(x); }
};
__attribute__((always_inline)) inline bool IS(char x) {
  return x == 10 || x == 13 || x == ' ';
}
template <typename T>
struct Fr {
  T P;
  __attribute__((always_inline)) inline Fr &operator,(int &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (f) x = -x;
    return *this;
  }
  __attribute__((always_inline)) inline operator int() {
    int x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(long long &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (f) x = -x;
    return *this;
  }
  __attribute__((always_inline)) inline operator long long() {
    long long x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(char &x) {
    for (x = P(); IS(x); x = P())
      ;
    return *this;
  }
  __attribute__((always_inline)) inline operator char() {
    char x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(char *x) {
    char t = P();
    for (; IS(t); t = P())
      ;
    if (~t) {
      for (; !IS(t) && ~t; t = P()) *x++ = t;
    }
    *x++ = 0;
    return *this;
  }
  __attribute__((always_inline)) inline Fr &operator,(double &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (t == '.') {
      double u = 0.1;
      for (t = P(); t >= '0' && t <= '9'; t = P(), u *= 0.1) x += u * (t - '0');
    }
    if (f) x = -x;
    return *this;
  }
  __attribute__((always_inline)) inline operator double() {
    double x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(long double &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (t == '.') {
      double u = 0.1;
      for (t = P(); t >= '0' && t <= '9'; t = P(), u *= 0.1) x += u * (t - '0');
    }
    if (f) x = -x;
    return *this;
  }
  __attribute__((always_inline)) inline operator long double() {
    long double x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(unsigned int &x) {
    x = 0;
    unsigned char t = P();
    while (t < '0' || t > '9') t = P();
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    return *this;
  }
  __attribute__((always_inline)) inline operator unsigned int() {
    unsigned int x;
    *this, x;
    return x;
  }
  __attribute__((always_inline)) inline Fr &operator,(unsigned long long &x) {
    x = 0;
    unsigned char t = P();
    while (t < '0' || t > '9') t = P();
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    return *this;
  }
  __attribute__((always_inline)) inline operator unsigned long long() {
    unsigned long long x;
    *this, x;
    return x;
  }
};
Fr<Cg> in;
template <typename T>
struct Fw {
  T P;
  __attribute__((always_inline)) inline Fw &operator,(int x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(int x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator,(unsigned int x) {
    if (x) {
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(unsigned int x) {
    if (x) {
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator,(long long x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[19], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(long long x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[19], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator,(unsigned long long x) {
    if (x) {
      unsigned char s[20], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(unsigned long long x) {
    if (x) {
      unsigned char s[20], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator,(char x) {
    P(x);
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(char x) {
    P(x);
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator,(const char *x) {
    while (*x) P(*x++);
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(const char *x) {
    while (*x) P(*x++);
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(double x, int y) {
    if (y) {
      double t = 0.5;
      for (int i = y; i--;) t *= 0.1;
      if (x >= 0)
        x += t;
      else
        x -= t, P('-');
      *this, (long long)(abs(x));
      P('.');
      if (x < 0) x = -x;
      while (y--) {
        x *= 10;
        x -= floor(x * 0.1) * 10;
        P(((int)x) % 10 + '0');
      }
    } else if (x >= 0)
      *this, (long long)(x + 0.5);
    else
      *this, (long long)(x - 0.5);
    ;
    return *this;
  }
  __attribute__((always_inline)) inline Fw &operator()(long double x, int y) {
    if (y) {
      double t = 0.5;
      for (int i = y; i--;) t *= 0.1;
      if (x >= 0)
        x += t;
      else
        x -= t, P('-');
      *this, (long long)(abs(x));
      P('.');
      if (x < 0) x = -x;
      while (y--) {
        x *= 10;
        x -= floor(x * 0.1) * 10;
        P(((int)x) % 10 + '0');
      }
    } else if (x >= 0)
      *this, (long long)(x + 0.5);
    else
      *this, (long long)(x - 0.5);
    ;
    return *this;
  }
};
Fw<Cp> out;
struct vec {
  double x, y;
  vec() {}
  vec(double a, double b) { x = a, y = b; }
  inline vec &operator+=(const vec &a) {
    x += a.x, y += a.y;
    return *this;
  }
  inline vec &operator-=(const vec &a) {
    x -= a.x, y -= a.y;
    return *this;
  }
  inline vec &operator/=(const double &a) {
    x /= a, y /= a;
    return *this;
  }
  inline vec &operator*=(const double &a) {
    x *= a, y *= a;
    return *this;
  }
  inline vec operator+(const vec &b) const {
    vec a = *this;
    a += b;
    return a;
  }
  inline vec operator-(const vec &b) const {
    vec a = *this;
    a -= b;
    return a;
  }
  inline vec operator/(const double &b) const {
    vec a = *this;
    a /= b;
    return a;
  }
  inline vec operator*(const double &b) const {
    vec a = *this;
    a *= b;
    return a;
  }
  inline double operator*(const vec &a) const { return x * a.x + y * a.y; }
  inline double operator%(const vec &a) const { return x * a.y - y * a.x; }
  inline double sqrd() const { return sqr(x) + sqr(y); }
  inline double d() { return sqrt(sqrd()); }
  inline double a() { return atan2(y, x); }
};
inline double sqrdis(const vec &a, const vec &b) {
  return sqr(a.x - b.x) + sqr(a.y - b.y);
}
inline double dis(const vec &a, const vec &b) { return sqrt(sqrdis(a, b)); }
inline vec rotl(const vec &a) { return vec(-a.y, a.x); }
inline vec rotr(const vec &a) { return vec(a.y, -a.x); }
struct line {
  vec a, b;
  line() {}
  line(vec x, vec y) { a = x, b = y; }
};
inline double intf(const line &a, const line &b) {
  return (b.b % (a.a - b.a)) / (a.b % b.b);
}
inline vec intsec(const line &a, const line &b) {
  return a.a + a.b * intf(a, b);
}
inline line rotl(const line &a) { return line(a.a, rotl(a.b)); }
inline line rotr(const line &a) { return line(a.a, rotr(a.b)); }
const int N = 100007;
const double pi = acos(-1), eps = 1e-8;
vec s[N], a[N];
int n, q[N * 2], nxt[N], pre[N];
bool vis[N];
double r;
inline int getconvex(vec *s, vec *t, int n) {
  std::sort(s, s + n, [&](vec x, vec y) {
    return x.x < y.x || (x.x == y.x && x.y < y.y);
  });
  int qe = 1;
  q[0] = 0;
  for (int i = 1, iend = n - 1; i <= iend; i++) {
    for (; qe > 1 && (s[i] - s[q[qe - 2]]) % (s[q[qe - 1]] - s[q[qe - 2]]) >= 0;
         qe--)
      ;
    q[qe++] = i;
  }
  int te = qe;
  for (int i = (n - 1) - 1; ~i; i--) {
    for (;
         qe > te && (s[i] - s[q[qe - 2]]) % (s[q[qe - 1]] - s[q[qe - 2]]) >= 0;
         qe--)
      ;
    q[qe++] = i;
  }
  assert(q[qe - 1] == 0 && qe - 1 <= n);
  for (int i = 0, iend = qe - 1; i < iend; i++) t[i] = s[q[i]];
  return qe - 1;
}
inline bool chk(vec *s, int x) {
  vec a = s[x], b = s[pre[x]], c = s[nxt[x]];
  vec t = (c - b) / 2;
  double td = t.d();
  if (abs(td) < eps) return 0;
  vec u = vec(-t.y, t.x) * sqrt(r * r - td * td) / td;
  return dis(b + t + u, a) <= r;
}
inline int getsec(vec *s, vec *t, int n) {
  for (int i = 0, iend = n; i < iend; i++)
    nxt[i] = (i + 1) % n, pre[(i + 1) % n] = i;
  int qe = 0;
  for (int i = 0, iend = n; i < iend; i++) q[qe++] = i;
  for (int i = 0; i < qe; i++) {
    if (!vis[q[i]] && chk(s, q[i])) {
      q[qe++] = nxt[q[i]];
      q[qe++] = pre[q[i]];
      nxt[pre[q[i]]] = nxt[q[i]];
      pre[nxt[q[i]]] = pre[q[i]];
      vis[q[i]] = 1;
    }
  }
  int c = 0;
  for (int i = 0, iend = n; i < iend; i++)
    if (!vis[i]) t[c++] = s[i];
  return c;
}
inline double getxa(double x) {
  double h = sqrt(r * r - sqr(x / 2));
  double a = asin(x / 2 / r);
  return r * r * a - x * h / 2;
}
int main() {
  in, n, r;
  if (n == 1) {
    out, 0, '\n';
    return 0;
  }
  for (int i = 0, iend = n; i < iend; i++) in, s[i].x, s[i].y;
  n = getconvex(s, a, n);
  n = getsec(a, s, n);
  s[n] = s[0];
  double ans = 0;
  for (int i = 0, iend = n; i < iend; i++) ans += getxa(dis(s[i], s[i + 1]));
  for (int i = 1, iend = n - 1; i <= iend; i++)
    ans += abs((s[i + 1] - s[i]) % (s[i] - s[0])) / 2;
  printf("%.10lf\n", ans);
}