#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 10;
int n, k;
int x[N], y[N], id[N];
int cmp(int a, int b) {
  if (x[a] == x[b]) return y[a] < y[b];
  return x[a] < x[b];
}
long long cross(int a, int o, int b) {
  return 1ll * (x[a] - x[o]) * (y[b] - y[o]) -
         1ll * (x[b] - x[o]) * (y[a] - y[o]);
}
double dist(int a, int b) {
  return sqrt(1ll * (x[a] - x[b]) * (x[a] - x[b]) +
              1ll * (y[a] - y[b]) * (y[a] - y[b]));
}
int check(int a, int b) {
  for (int i = 1; i <= n; i++) {
    if (i == a || i == b) continue;
    if (cross(a, b, i)) return 0;
  }
  return 1;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> x[i] >> y[i], id[i] = i;
  if (check(id[2], id[3]))
    swap(id[1], id[3]);
  else if (check(id[1], id[3]))
    swap(id[2], id[3]);
  int out = -1;
  for (int i = 3; i <= n; i++)
    if (cross(id[1], id[2], id[i])) out = id[i];
  swap(id[out], id[n]);
  sort(id + 1, id + n, cmp);
  cout.precision(20), cout << fixed;
  if (k == id[n]) {
    cout << dist(id[1], id[n - 1]) +
                min(dist(id[1], id[n]), dist(id[n - 1], id[n]))
         << endl;
    return 0;
  }
  int pos = -1;
  for (int i = 1; i < n; i++)
    if (id[i] == k) pos = i;
  double res = 1.0 / 0.0;
  double mn = dist(id[n - 1], id[n]);
  if (pos + 1 < n) {
    mn = min(mn, dist(id[n], id[1]) + dist(id[n], id[pos + 1]) -
                     dist(id[1], id[pos + 1]));
    for (int i = pos + 2; i < n; i++)
      mn = min(mn, dist(id[i - 1], id[n]) + dist(id[i], id[n]) -
                       dist(id[i], id[i - 1]));
  }
  res = min(res, dist(id[1], id[pos]) + dist(id[1], id[n - 1]) + mn);
  mn = dist(id[1], id[n]);
  if (pos - 1 >= 1) {
    mn = min(mn, dist(id[n], id[n - 1]) + dist(id[n], id[pos - 1]) -
                     dist(id[n - 1], id[pos - 1]));
    for (int i = 2; i < pos; i++)
      mn = min(mn, dist(id[i - 1], id[n]) + dist(id[i], id[n]) -
                       dist(id[i], id[i - 1]));
  }
  res = min(res, dist(id[n - 1], id[pos]) + dist(id[1], id[n - 1]) + mn);
  cout << res << endl;
  return 0;
}

### Prompt

Your task is to create 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 N = 1e6 + 10;
int n, k;
int x[N], y[N], id[N];
int cmp(int a, int b) {
  if (x[a] == x[b]) return y[a] < y[b];
  return x[a] < x[b];
}
long long cross(int a, int o, int b) {
  return 1ll * (x[a] - x[o]) * (y[b] - y[o]) -
         1ll * (x[b] - x[o]) * (y[a] - y[o]);
}
double dist(int a, int b) {
  return sqrt(1ll * (x[a] - x[b]) * (x[a] - x[b]) +
              1ll * (y[a] - y[b]) * (y[a] - y[b]));
}
int check(int a, int b) {
  for (int i = 1; i <= n; i++) {
    if (i == a || i == b) continue;
    if (cross(a, b, i)) return 0;
  }
  return 1;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> x[i] >> y[i], id[i] = i;
  if (check(id[2], id[3]))
    swap(id[1], id[3]);
  else if (check(id[1], id[3]))
    swap(id[2], id[3]);
  int out = -1;
  for (int i = 3; i <= n; i++)
    if (cross(id[1], id[2], id[i])) out = id[i];
  swap(id[out], id[n]);
  sort(id + 1, id + n, cmp);
  cout.precision(20), cout << fixed;
  if (k == id[n]) {
    cout << dist(id[1], id[n - 1]) +
                min(dist(id[1], id[n]), dist(id[n - 1], id[n]))
         << endl;
    return 0;
  }
  int pos = -1;
  for (int i = 1; i < n; i++)
    if (id[i] == k) pos = i;
  double res = 1.0 / 0.0;
  double mn = dist(id[n - 1], id[n]);
  if (pos + 1 < n) {
    mn = min(mn, dist(id[n], id[1]) + dist(id[n], id[pos + 1]) -
                     dist(id[1], id[pos + 1]));
    for (int i = pos + 2; i < n; i++)
      mn = min(mn, dist(id[i - 1], id[n]) + dist(id[i], id[n]) -
                       dist(id[i], id[i - 1]));
  }
  res = min(res, dist(id[1], id[pos]) + dist(id[1], id[n - 1]) + mn);
  mn = dist(id[1], id[n]);
  if (pos - 1 >= 1) {
    mn = min(mn, dist(id[n], id[n - 1]) + dist(id[n], id[pos - 1]) -
                     dist(id[n - 1], id[pos - 1]));
    for (int i = 2; i < pos; i++)
      mn = min(mn, dist(id[i - 1], id[n]) + dist(id[i], id[n]) -
                       dist(id[i], id[i - 1]));
  }
  res = min(res, dist(id[n - 1], id[pos]) + dist(id[1], id[n - 1]) + mn);
  cout << res << endl;
  return 0;
}

```