#include <bits/stdc++.h>
using namespace std;
const int MAXN = (int)2e5 + 5;
const double oo = 1e9 + 7;
struct pt {
  long long x, y;
  pt operator+(pt p) { return {x + p.x, y + p.y}; }
  pt operator-(pt p) { return {x - p.x, y - p.y}; }
  long long operator*(pt p) { return x * p.y - y * p.x; }
  long long operator|(pt p) { return x * p.x + y * p.y; }
  bool inline operator==(const pt &rhs) const {
    return x == rhs.x && y == rhs.y;
  }
};
struct line {
  pt v;
  long long c;
  line(pt p, pt q) : v(q - p), c(v * p) {}
  bool is_on(pt p) { return v * p == c; }
};
int n, k;
pt p[MAXN];
line find_line() {
  for (int i = 0; i < 3; ++i) {
    for (int j = i + 1; j < 3; ++j) {
      line l(p[i], p[j]);
      int cnt = 0;
      for (int t = 0; t < n; ++t)
        if (l.is_on(p[t])) ++cnt;
      if (cnt == n - 1) return l;
    }
  }
  cerr << "Line not found" << endl;
  exit(0);
}
int main() {
  cin >> n >> k;
  --k;
  for (int i = 0; i < n; ++i) cin >> p[i].x >> p[i].y;
  pt save = p[k];
  line l = find_line();
  for (int i = 0; i < n; ++i) {
    if (!l.is_on(p[i])) {
      swap(p[i], p[n - 1]);
      break;
    }
  }
  --n;
  auto proj_cmp = [&](pt p, pt q) { return (l.v | p) < (l.v | q); };
  sort(p, p + n, proj_cmp);
  auto dist = [&](int i, int j) {
    return hypot(p[i].x - p[j].x, p[i].y - p[j].y);
  };
  auto cover = [&](int l, int r) {
    return min(dist(l, n), dist(r, n)) + dist(l, r);
  };
  for (int i = 0; i <= n; ++i) {
    if (p[i] == save) {
      k = i;
      break;
    }
  }
  double ans = oo;
  if (k == n)
    ans = cover(0, n - 1);
  else {
    for (int i = 0; i <= k; ++i) {
      double d = min(dist(k, i) + dist(n - 1, n), dist(k, n - 1) + dist(i, n)) +
                 dist(i, n - 1);
      if (i > 0) d += cover(0, i - 1);
      ans = min(ans, d);
    }
    for (int i = k; i < n; ++i) {
      double d =
          min(dist(k, i) + dist(0, n), dist(k, 0) + dist(i, n)) + dist(0, i);
      if (i < n - 1) d += cover(i + 1, n - 1);
      ans = min(ans, d);
    }
  }
  printf("%.15g\n", ans);
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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;
const int MAXN = (int)2e5 + 5;
const double oo = 1e9 + 7;
struct pt {
  long long x, y;
  pt operator+(pt p) { return {x + p.x, y + p.y}; }
  pt operator-(pt p) { return {x - p.x, y - p.y}; }
  long long operator*(pt p) { return x * p.y - y * p.x; }
  long long operator|(pt p) { return x * p.x + y * p.y; }
  bool inline operator==(const pt &rhs) const {
    return x == rhs.x && y == rhs.y;
  }
};
struct line {
  pt v;
  long long c;
  line(pt p, pt q) : v(q - p), c(v * p) {}
  bool is_on(pt p) { return v * p == c; }
};
int n, k;
pt p[MAXN];
line find_line() {
  for (int i = 0; i < 3; ++i) {
    for (int j = i + 1; j < 3; ++j) {
      line l(p[i], p[j]);
      int cnt = 0;
      for (int t = 0; t < n; ++t)
        if (l.is_on(p[t])) ++cnt;
      if (cnt == n - 1) return l;
    }
  }
  cerr << "Line not found" << endl;
  exit(0);
}
int main() {
  cin >> n >> k;
  --k;
  for (int i = 0; i < n; ++i) cin >> p[i].x >> p[i].y;
  pt save = p[k];
  line l = find_line();
  for (int i = 0; i < n; ++i) {
    if (!l.is_on(p[i])) {
      swap(p[i], p[n - 1]);
      break;
    }
  }
  --n;
  auto proj_cmp = [&](pt p, pt q) { return (l.v | p) < (l.v | q); };
  sort(p, p + n, proj_cmp);
  auto dist = [&](int i, int j) {
    return hypot(p[i].x - p[j].x, p[i].y - p[j].y);
  };
  auto cover = [&](int l, int r) {
    return min(dist(l, n), dist(r, n)) + dist(l, r);
  };
  for (int i = 0; i <= n; ++i) {
    if (p[i] == save) {
      k = i;
      break;
    }
  }
  double ans = oo;
  if (k == n)
    ans = cover(0, n - 1);
  else {
    for (int i = 0; i <= k; ++i) {
      double d = min(dist(k, i) + dist(n - 1, n), dist(k, n - 1) + dist(i, n)) +
                 dist(i, n - 1);
      if (i > 0) d += cover(0, i - 1);
      ans = min(ans, d);
    }
    for (int i = k; i < n; ++i) {
      double d =
          min(dist(k, i) + dist(0, n), dist(k, 0) + dist(i, n)) + dist(0, i);
      if (i < n - 1) d += cover(i + 1, n - 1);
      ans = min(ans, d);
    }
  }
  printf("%.15g\n", ans);
  return 0;
}

```