#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
struct TPoint {
  T x;
  T y;
  int id;
  TPoint() : x(0), y(0), id(-1) {}
  TPoint(const T& x_, const T& y_) : x(x_), y(y_), id(-1) {}
  TPoint(const T& x_, const T& y_, int id_) : x(x_), y(y_), id(id_) {}
  static constexpr T eps = static_cast<T>(1e-9);
  inline TPoint operator+(const TPoint& rhs) const {
    return TPoint(x + rhs.x, y + rhs.y);
  }
  inline TPoint operator-(const TPoint& rhs) const {
    return TPoint(x - rhs.x, y - rhs.y);
  }
  inline TPoint operator*(const T& rhs) const {
    return TPoint(x * rhs, y * rhs);
  }
  inline TPoint operator/(const T& rhs) const {
    return TPoint(x / rhs, y / rhs);
  }
  friend T smul(const TPoint& a, const TPoint& b) {
    return a.x * b.x + a.y * b.y;
  }
  friend T vmul(const TPoint& a, const TPoint& b) {
    return a.x * b.y - a.y * b.x;
  }
  inline T abs2() const { return x * x + y * y; }
  inline bool operator<(const TPoint& rhs) const {
    return (y < rhs.y || (y == rhs.y && x < rhs.x));
  }
  inline bool is_upper() const {
    return (y > eps || (abs(y) <= eps && x > eps));
  }
  inline int cmp_polar(const TPoint& rhs) const {
    assert(abs(x) > eps || abs(y) > eps);
    assert(abs(rhs.x) > eps || abs(rhs.y) > eps);
    bool a = is_upper();
    bool b = rhs.is_upper();
    if (a != b) {
      return (a ? -1 : 1);
    }
    long long v = x * rhs.y - y * rhs.x;
    return (v > eps ? -1 : (v < -eps ? 1 : 0));
  }
};
using Point = TPoint<long long>;
template <typename T>
string to_string(const TPoint<T>& p) {
  return "(" + to_string(p.x) + ", " + to_string(p.y) + ")";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<Point> p(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i].x >> p[i].y;
  }
  vector<vector<long long>> area(n, vector<long long>(n, 0));
  for (int i = 0; i < n; i++) {
    for (int k = 2; k <= n - 1; k++) {
      int x = (i + k - 1) % n;
      int y = (i + k) % n;
      area[i][y] = area[i][x] + abs(vmul(p[x] - p[i], p[y] - p[i]));
    }
  }
  42;
  if (k == 0) {
    cout << area[0][n - 1] << '\n';
    return 0;
  }
  long long low = 0;
  long long high = (long long)4e18;
  while (low < high) {
    long long mid = (low + high + 1) >> 1;
    const int inf = (int)1e6;
    vector<vector<int>> dp(n, vector<int>(n, -inf));
    for (int len = 1; len <= n - 1; len++) {
      for (int i = 0; i < n; i++) {
        int j = (i + len) % n;
        if (area[i][j] >= mid) {
          dp[i][j] = 0;
        }
        for (int q = 2; q <= len - 2; q++) {
          int u = (i + q) % n;
          if (area[i][j] - area[i][u] - area[u][j] >= mid) {
            dp[i][j] = max(dp[i][j], dp[i][u] + dp[u][j] + 2);
          }
        }
        int p = 0;
        for (int q = 0; q <= len - 2; q++) {
          int u = (i + q) % n;
          p = max(p, q);
          while (p < len) {
            int v = (i + p + 1) % n;
            if (area[i][j] - area[u][v] >= mid) {
              ++p;
            } else {
              break;
            }
          }
          int v = (i + p) % n;
          if (area[i][j] - area[u][v] >= mid) {
            dp[i][j] = max(dp[i][j], dp[u][v] + 1);
          }
        }
        42;
      }
    }
    bool ok = false;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (dp[i][j] + dp[j][i] + 1 >= k) {
          ok = true;
          break;
        }
      }
      if (ok) break;
    }
    if (ok) {
      low = mid;
    } else {
      high = mid - 1;
    }
  }
  cout << low << '\n';
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

You are given a strictly convex polygon with n vertices.

You will make k cuts that meet the following conditions: 

  * each cut is a segment that connects two different nonadjacent vertices; 
  * two cuts can intersect only at vertices of the polygon. 



Your task is to maximize the area of the smallest region that will be formed by the polygon and those k cuts.

Input

The first line contains two integers n, k (3 ≤ n ≤ 200, 0 ≤ k ≤ n-3).

The following n lines describe vertices of the polygon in anticlockwise direction. The i-th line contains two integers x_i, y_i (|x_i|, |y_i| ≤ 10^8) — the coordinates of the i-th vertex.

It is guaranteed that the polygon is convex and that no two adjacent sides are parallel.

Output

Print one integer: the maximum possible area of the smallest region after making k cuts multiplied by 2.

Examples

Input


8 4
-2 -4
2 -2
4 2
1 5
0 5
-4 4
-5 0
-5 -1


Output


11


Input


6 3
2 -2
2 -1
1 2
0 2
-2 1
-1 0


Output


3

Note

In the first example, it's optimal to make cuts between the following pairs of vertices: 

  * (-2, -4) and (4, 2), 
  * (-2, -4) and (1, 5), 
  * (-5, -1) and (1, 5), 
  * (-5, 0) and (0, 5). 

<image> Points (-5, -1), (1, 5), (0, 5), (-5, 0) determine the smallest region with double area of 11. 

In the second example, it's optimal to make cuts between the following pairs of vertices: 

  * (2, -1) and (0, 2), 
  * (2, -1) and (1, 0), 
  * (-1, 0) and (0, 2). 

<image> Points (2, -2), (2, -1), (-1, 0) determine one of the smallest regions with double area of 3. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T>
struct TPoint {
  T x;
  T y;
  int id;
  TPoint() : x(0), y(0), id(-1) {}
  TPoint(const T& x_, const T& y_) : x(x_), y(y_), id(-1) {}
  TPoint(const T& x_, const T& y_, int id_) : x(x_), y(y_), id(id_) {}
  static constexpr T eps = static_cast<T>(1e-9);
  inline TPoint operator+(const TPoint& rhs) const {
    return TPoint(x + rhs.x, y + rhs.y);
  }
  inline TPoint operator-(const TPoint& rhs) const {
    return TPoint(x - rhs.x, y - rhs.y);
  }
  inline TPoint operator*(const T& rhs) const {
    return TPoint(x * rhs, y * rhs);
  }
  inline TPoint operator/(const T& rhs) const {
    return TPoint(x / rhs, y / rhs);
  }
  friend T smul(const TPoint& a, const TPoint& b) {
    return a.x * b.x + a.y * b.y;
  }
  friend T vmul(const TPoint& a, const TPoint& b) {
    return a.x * b.y - a.y * b.x;
  }
  inline T abs2() const { return x * x + y * y; }
  inline bool operator<(const TPoint& rhs) const {
    return (y < rhs.y || (y == rhs.y && x < rhs.x));
  }
  inline bool is_upper() const {
    return (y > eps || (abs(y) <= eps && x > eps));
  }
  inline int cmp_polar(const TPoint& rhs) const {
    assert(abs(x) > eps || abs(y) > eps);
    assert(abs(rhs.x) > eps || abs(rhs.y) > eps);
    bool a = is_upper();
    bool b = rhs.is_upper();
    if (a != b) {
      return (a ? -1 : 1);
    }
    long long v = x * rhs.y - y * rhs.x;
    return (v > eps ? -1 : (v < -eps ? 1 : 0));
  }
};
using Point = TPoint<long long>;
template <typename T>
string to_string(const TPoint<T>& p) {
  return "(" + to_string(p.x) + ", " + to_string(p.y) + ")";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<Point> p(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i].x >> p[i].y;
  }
  vector<vector<long long>> area(n, vector<long long>(n, 0));
  for (int i = 0; i < n; i++) {
    for (int k = 2; k <= n - 1; k++) {
      int x = (i + k - 1) % n;
      int y = (i + k) % n;
      area[i][y] = area[i][x] + abs(vmul(p[x] - p[i], p[y] - p[i]));
    }
  }
  42;
  if (k == 0) {
    cout << area[0][n - 1] << '\n';
    return 0;
  }
  long long low = 0;
  long long high = (long long)4e18;
  while (low < high) {
    long long mid = (low + high + 1) >> 1;
    const int inf = (int)1e6;
    vector<vector<int>> dp(n, vector<int>(n, -inf));
    for (int len = 1; len <= n - 1; len++) {
      for (int i = 0; i < n; i++) {
        int j = (i + len) % n;
        if (area[i][j] >= mid) {
          dp[i][j] = 0;
        }
        for (int q = 2; q <= len - 2; q++) {
          int u = (i + q) % n;
          if (area[i][j] - area[i][u] - area[u][j] >= mid) {
            dp[i][j] = max(dp[i][j], dp[i][u] + dp[u][j] + 2);
          }
        }
        int p = 0;
        for (int q = 0; q <= len - 2; q++) {
          int u = (i + q) % n;
          p = max(p, q);
          while (p < len) {
            int v = (i + p + 1) % n;
            if (area[i][j] - area[u][v] >= mid) {
              ++p;
            } else {
              break;
            }
          }
          int v = (i + p) % n;
          if (area[i][j] - area[u][v] >= mid) {
            dp[i][j] = max(dp[i][j], dp[u][v] + 1);
          }
        }
        42;
      }
    }
    bool ok = false;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (dp[i][j] + dp[j][i] + 1 >= k) {
          ok = true;
          break;
        }
      }
      if (ok) break;
    }
    if (ok) {
      low = mid;
    } else {
      high = mid - 1;
    }
  }
  cout << low << '\n';
  return 0;
}

```