#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const double eps = 0.000001;
const int N = 300000;
bool isti(double x, double y) { return abs(x - y) < eps; }
struct Point {
  double x, y;
  bool operator<(const Point &g) {
    if (isti(x, g.x)) return y < g.y;
    return x < g.x;
  }
  bool operator==(const Point &g) { return isti(x, g.x) && isti(y, g.y); }
};
double cross(Point a, Point b, Point c) {
  return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
bool collinear(Point a, Point b, Point c) { return isti(cross(a, b, c), 0); }
Point _p[N + 5];
double dist(Point a, Point b) {
  return sqrtl((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
void brut(int n) {
  if (n == 1)
    cout << "0\n";
  else if (n == 2)
    cout << dist(_p[1], _p[2]) << "\n";
  else
    cout << dist(_p[1], _p[2]) + dist(_p[1], _p[3]) + dist(_p[2], _p[3]) -
                max(dist(_p[1], _p[2]), dist(_p[1], _p[3]))
         << "\n";
}
bool cmp(pair<Point, int> x, pair<Point, int> y) {
  if (x.first == y.first) return x.second < y.second;
  return x.first < y.first;
}
vector<Point> p;
int bad = 0;
Point bp;
double solve(int l, int r) {
  if (l > r) return 0;
  return dist(p[l], p[r]) + min(dist(bp, p[l]), dist(bp, p[r]));
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0);
  cout.precision(10);
  cout << fixed;
  int n, st;
  cin >> n >> st;
  for (int i = 1; i <= n; i++) {
    int x, y;
    cin >> x >> y;
    _p[i].x = x;
    _p[i].y = y;
  }
  swap(_p[1], _p[st]);
  if (n <= 3) {
    brut(n);
    return 0;
  }
  Point g1 = {0, 0}, g2 = {0, 0};
  bool xd = 0;
  if (collinear(_p[1], _p[2], _p[3])) xd = 1, g1 = _p[1], g2 = _p[2];
  if (collinear(_p[1], _p[2], _p[4])) xd = 1, g1 = _p[1], g2 = _p[2];
  if (collinear(_p[1], _p[3], _p[4])) xd = 1, g1 = _p[1], g2 = _p[3];
  if (collinear(_p[2], _p[3], _p[4])) xd = 1, g1 = _p[2], g2 = _p[3];
  assert(xd);
  vector<pair<Point, int>> pp;
  for (int i = 1; i <= n; i++) {
    if (collinear(g1, g2, _p[i])) {
      pp.push_back({_p[i], i});
    } else
      bad = i;
  }
  assert(bad);
  bp = _p[bad];
  sort(pp.begin(), pp.end(), cmp);
  assert(pp.size() == n - 1);
  int poc = -1;
  for (auto c : pp) {
    p.push_back(c.first);
    if (c.second == 1) poc = int(p.size()) - 1;
  }
  assert(p.size() == n - 1);
  n = p.size();
  if (bad == 1) {
    cout << solve(0, n - 1) << "\n";
    return 0;
  }
  double res = solve(0, n - 1) + dist(p[poc], bp);
  for (int i = 1; i < n - 1; i++) {
    res = min(res, dist(p[poc], p[i]) + dist(p[i], bp) + solve(0, n - 1));
  }
  res = min(res, dist(p[poc], p[0]) + dist(p[0], bp) + solve(poc + 1, n - 1));
  res =
      min(res, dist(p[poc], p[n - 1]) + dist(p[n - 1], bp) + solve(0, poc - 1));
  for (int i = poc + 1; i < n; i++) {
    res = min(res, dist(p[poc], p[0]) + dist(p[0], p[i]) + dist(p[i], bp) +
                       solve(i + 1, n - 1));
  }
  for (int i = poc - 1; i >= 0; i--) {
    res = min(res, dist(p[poc], p[n - 1]) + dist(p[n - 1], p[i]) +
                       dist(p[i], bp) + solve(0, i - 1));
  }
  cout << res << "\n";
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

You are given N points on an infinite plane with the Cartesian coordinate system on it. N-1 points lay on one line, and one point isn't on that line. You are on point K at the start, and the goal is to visit every point. You can move between any two points in a straight line, and you can revisit points. What is the minimum length of the path? 

Input

The first line contains two integers: N (3 ≤ N ≤ 2*10^5) - the number of points, and K (1 ≤ K ≤ N) - the index of the starting point.

Each of the next N lines contain two integers, A_i, B_i (-10^6 ≤ A_i, B_i ≤ 10^6) - coordinates of the i-th point.

Output

The output contains one number - the shortest path to visit all given points starting from point K. The absolute difference between your solution and the main solution shouldn't exceed 10^-6;

Example

Input


5 2
0 0
-1 1
2 -2
0 1
-2 2


Output


7.478709

Note

The shortest path consists of these moves: 

2 -> 5 

5 -> 4 

4 -> 1 

1 -> 3 

There isn't any shorter path possible.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const double eps = 0.000001;
const int N = 300000;
bool isti(double x, double y) { return abs(x - y) < eps; }
struct Point {
  double x, y;
  bool operator<(const Point &g) {
    if (isti(x, g.x)) return y < g.y;
    return x < g.x;
  }
  bool operator==(const Point &g) { return isti(x, g.x) && isti(y, g.y); }
};
double cross(Point a, Point b, Point c) {
  return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
bool collinear(Point a, Point b, Point c) { return isti(cross(a, b, c), 0); }
Point _p[N + 5];
double dist(Point a, Point b) {
  return sqrtl((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
void brut(int n) {
  if (n == 1)
    cout << "0\n";
  else if (n == 2)
    cout << dist(_p[1], _p[2]) << "\n";
  else
    cout << dist(_p[1], _p[2]) + dist(_p[1], _p[3]) + dist(_p[2], _p[3]) -
                max(dist(_p[1], _p[2]), dist(_p[1], _p[3]))
         << "\n";
}
bool cmp(pair<Point, int> x, pair<Point, int> y) {
  if (x.first == y.first) return x.second < y.second;
  return x.first < y.first;
}
vector<Point> p;
int bad = 0;
Point bp;
double solve(int l, int r) {
  if (l > r) return 0;
  return dist(p[l], p[r]) + min(dist(bp, p[l]), dist(bp, p[r]));
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0);
  cout.precision(10);
  cout << fixed;
  int n, st;
  cin >> n >> st;
  for (int i = 1; i <= n; i++) {
    int x, y;
    cin >> x >> y;
    _p[i].x = x;
    _p[i].y = y;
  }
  swap(_p[1], _p[st]);
  if (n <= 3) {
    brut(n);
    return 0;
  }
  Point g1 = {0, 0}, g2 = {0, 0};
  bool xd = 0;
  if (collinear(_p[1], _p[2], _p[3])) xd = 1, g1 = _p[1], g2 = _p[2];
  if (collinear(_p[1], _p[2], _p[4])) xd = 1, g1 = _p[1], g2 = _p[2];
  if (collinear(_p[1], _p[3], _p[4])) xd = 1, g1 = _p[1], g2 = _p[3];
  if (collinear(_p[2], _p[3], _p[4])) xd = 1, g1 = _p[2], g2 = _p[3];
  assert(xd);
  vector<pair<Point, int>> pp;
  for (int i = 1; i <= n; i++) {
    if (collinear(g1, g2, _p[i])) {
      pp.push_back({_p[i], i});
    } else
      bad = i;
  }
  assert(bad);
  bp = _p[bad];
  sort(pp.begin(), pp.end(), cmp);
  assert(pp.size() == n - 1);
  int poc = -1;
  for (auto c : pp) {
    p.push_back(c.first);
    if (c.second == 1) poc = int(p.size()) - 1;
  }
  assert(p.size() == n - 1);
  n = p.size();
  if (bad == 1) {
    cout << solve(0, n - 1) << "\n";
    return 0;
  }
  double res = solve(0, n - 1) + dist(p[poc], bp);
  for (int i = 1; i < n - 1; i++) {
    res = min(res, dist(p[poc], p[i]) + dist(p[i], bp) + solve(0, n - 1));
  }
  res = min(res, dist(p[poc], p[0]) + dist(p[0], bp) + solve(poc + 1, n - 1));
  res =
      min(res, dist(p[poc], p[n - 1]) + dist(p[n - 1], bp) + solve(0, poc - 1));
  for (int i = poc + 1; i < n; i++) {
    res = min(res, dist(p[poc], p[0]) + dist(p[0], p[i]) + dist(p[i], bp) +
                       solve(i + 1, n - 1));
  }
  for (int i = poc - 1; i >= 0; i--) {
    res = min(res, dist(p[poc], p[n - 1]) + dist(p[n - 1], p[i]) +
                       dist(p[i], bp) + solve(0, i - 1));
  }
  cout << res << "\n";
  return 0;
}

```