A14587. Shortest path

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?

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

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

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 $10^-6$ ;

The shortest path consists of these moves:

2 -> 5

5 -> 4

4 -> 1

1 -> 3

There isn't any shorter path possible.