description: 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.
solution: //package bubblecup14;
  import java.io.*;
  import java.util.ArrayDeque;
  import java.util.Arrays;
  import java.util.InputMismatchException;
  import java.util.Queue;
  
  public class G {
  	InputStream is;
  	FastWriter out;
  	String INPUT = "";
  	
  	void solve()
  	{
  		int n = ni(), K = ni()-1;
  		int[][] co = new int[n][];
  		for(int i = 0;i < n;i++){
  			co[i] = na(2);
  		}
  
  		int X = 0;
  		if(n > 3) {
  			int arg = -1;
  			int nfal = 0;
  			for (int i = 2; i < n; i++) {
  				if(!onSameLine(co[0], co[1], co[i])){
  					nfal++;
  					arg = i;
  				}
  			}
  			if(nfal == 1){
  				X = arg;
  			}else{
  				arg = -1;
  				for (int i = 0; i < n; i++) {
  					if(i == 2 || i == 3)continue;
  					if(!onSameLine(co[2], co[3], co[i])){
  						arg = i;
  					}
  				}
  				assert arg != -1;
  				X = arg;
  			}
  		}
  
  		int NX = X == 0 ? 1 : 0;
  		int xx = co[NX][0];
  		int yy = co[NX][1];
  		for(int i = 0;i < n;i++){
  			co[i][0] -= xx;
  			co[i][1] -= yy;
  		}
  		int NNX = -1;
  		for(int i = 0;i < n;i++){
  			if(i == X || i == NX)continue;
  			NNX = i;
  			break;
  		}
  		assert NNX != -1;
  		double theta = Math.atan2(co[NNX][1], co[NNX][0]);
  
  		double[][] dco = new double[n][];
  		for(int i = 0;i < n;i++){
  			double[] u = new double[]{co[i][0], co[i][1]};
  			dco[i] = rotate(u, -theta);
  		}
  
  		double[] XX = dco[X];
  
  		double[] xs = new double[n-1];
  		int p = 0;
  		for(int i = 0;i < n;i++){
  			if(i != X){
  				xs[p++] = dco[i][0];
  			}
  		}
  		Arrays.sort(xs);
  		int ind = Arrays.binarySearch(xs, dco[K][0]);
  
  		if(K == X){
  			double ans = Double.POSITIVE_INFINITY;
  			ans = Math.min(ans,
  					d(XX, new double[]{xs[n-2], 0}) + (xs[n-2] - xs[0])
  			);
  			ans = Math.min(ans,
  					d(XX, new double[]{xs[0], 0}) + (xs[n-2] - xs[0])
  			);
  			out.println(ans, 14);
  		}else{
  			double ans = Double.POSITIVE_INFINITY;
  			if(ind > 0) {
  				ans = Math.min(ans,
  						d(XX, new double[]{xs[n - 2], 0}) + d(XX, new double[]{xs[0], 0}) + (xs[n - 2] - xs[0] - (xs[ind] - xs[ind - 1]))
  				);
  			}
  			if(ind+1 < n-1) {
  				ans = Math.min(ans,
  						d(XX, new double[]{xs[n - 2], 0}) + d(XX, new double[]{xs[0], 0}) + (xs[n - 2] - xs[0] - (xs[ind+1] - xs[ind]))
  				);
  			}
  			ans = Math.min(ans, (xs[n-2] - xs[ind]) + (xs[n-2] - xs[0]) + d(XX, new double[]{xs[0], 0}));
  			ans = Math.min(ans, (xs[ind] - xs[0]) + (xs[n-2] - xs[0]) + d(XX, new double[]{xs[n-2], 0}));
  			ans = Math.min(ans, (xs[n-2] - xs[0]) + d(XX, new double[]{xs[ind], 0}) + d(XX, new double[]{xs[n-2], 0}));
  			ans = Math.min(ans, (xs[n-2] - xs[0]) + d(XX, new double[]{xs[ind], 0}) + d(XX, new double[]{xs[0], 0}));
  			if(ind > 0){
  				ans = Math.min(ans, (xs[n-2] - xs[0] - (xs[ind] - xs[ind-1]) + d(XX, new double[]{xs[n-2], 0})) + d(XX, new double[]{xs[ind-1], 0}));
  			}
  			if(ind+1 < n-1){
  				ans = Math.min(ans, (xs[n-2] - xs[0] - (xs[ind+1] - xs[ind]) + d(XX, new double[]{xs[0], 0})) + d(XX, new double[]{xs[ind+1], 0}));
  			}
  			for(int i = 0;i < n-2;i++){
  				ans = Math.min(ans, (xs[n-2] - xs[ind]) + (xs[n-2] - xs[0]) - (xs[i+1] - xs[i]) + d(XX, new double[]{xs[i], 0}) + d(XX, new double[]{xs[i+1], 0}));
  				ans = Math.min(ans, (xs[ind] - xs[0]) + (xs[n-2] - xs[0]) - (xs[i+1] - xs[i]) + d(XX, new double[]{xs[i], 0}) + d(XX, new double[]{xs[i+1], 0}));
  			}
  			out.println(ans, 14);
  		}
  	}
  
  	double d(double[] a, double[] b)
  	{
  		return Math.sqrt(d2(a, b));
  	}
  
  	public static double d2(double[] a, double[] b)
  	{
  		return d2(a[0], a[1], b[0], b[1]);
  	}
  
  	public static double d2(double ax, double ay, double bx, double by)
  	{
  		return (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
  	}
  
  
  	public static double[] rotate(double[] co, double theta)
  	{
  		double cos = Math.cos(theta);
  		double sin = Math.sin(theta);
  		return new double[]{
  				co[0]*cos - co[1]*sin,
  				co[0]*sin + co[1]*cos
  		};
  	}
  
  	public static boolean onSameLine(int[] a, int[] b, int[] c)
  	{
  		return (long)(c[0]-a[0])*(b[1]-a[1])-(long)(c[1]-a[1])*(b[0]-a[0])==0;
  	}
  
  
  	void run() throws Exception
  	{
  		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
  		out = new FastWriter(System.out);
  		
  		long s = System.currentTimeMillis();
  		solve();
  		out.flush();
  		tr(System.currentTimeMillis()-s+"ms");
  	}
  	
  	public static void main(String[] args) throws Exception { new G().run(); }
  	
  	private byte[] inbuf = new byte[1024];
  	public int lenbuf = 0, ptrbuf = 0;
  	
  	private int readByte()
  	{
  		if(lenbuf == -1)throw new InputMismatchException();
  		if(ptrbuf >= lenbuf){
  			ptrbuf = 0;
  			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
  			if(lenbuf <= 0)return -1;
  		}
  		return inbuf[ptrbuf++];
  	}
  	
  	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
  	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
  	
  	private double nd() { return Double.parseDouble(ns()); }
  	private char nc() { return (char)skip(); }
  	
  	private String ns()
  	{
  		int b = skip();
  		StringBuilder sb = new StringBuilder();
  		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
  			sb.appendCodePoint(b);
  			b = readByte();
  		}
  		return sb.toString();
  	}
  	
  	private char[] ns(int n)
  	{
  		char[] buf = new char[n];
  		int b = skip(), p = 0;
  		while(p < n && !(isSpaceChar(b))){
  			buf[p++] = (char)b;
  			b = readByte();
  		}
  		return n == p ? buf : Arrays.copyOf(buf, p);
  	}
  
  	private int[] na(int n)
  	{
  		int[] a = new int[n];
  		for(int i = 0;i < n;i++)a[i] = ni();
  		return a;
  	}
  
  	private long[] nal(int n)
  	{
  		long[] a = new long[n];
  		for(int i = 0;i < n;i++)a[i] = nl();
  		return a;
  	}
  
  	private char[][] nm(int n, int m) {
  		char[][] map = new char[n][];
  		for(int i = 0;i < n;i++)map[i] = ns(m);
  		return map;
  	}
  
  	private int[][] nmi(int n, int m) {
  		int[][] map = new int[n][];
  		for(int i = 0;i < n;i++)map[i] = na(m);
  		return map;
  	}
  
  	private int ni() { return (int)nl(); }
  
  	private long nl()
  	{
  		long num = 0;
  		int b;
  		boolean minus = false;
  		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
  		if(b == '-'){
  			minus = true;
  			b = readByte();
  		}
  
  		while(true){
  			if(b >= '0' && b <= '9'){
  				num = num * 10 + (b - '0');
  			}else{
  				return minus ? -num : num;
  			}
  			b = readByte();
  		}
  	}
  
  	public static class FastWriter
  	{
  		private static final int BUF_SIZE = 1<<13;
  		private final byte[] buf = new byte[BUF_SIZE];
  		private final OutputStream out;
  		private int ptr = 0;
  
  		private FastWriter(){out = null;}
  
  		public FastWriter(OutputStream os)
  		{
  			this.out = os;
  		}
  
  		public FastWriter(String path)
  		{
  			try {
  				this.out = new FileOutputStream(path);
  			} catch (FileNotFoundException e) {
  				throw new RuntimeException("FastWriter");
  			}
  		}
  
  		public FastWriter write(byte b)
  		{
  			buf[ptr++] = b;
  			if(ptr == BUF_SIZE)innerflush();
  			return this;
  		}
  
  		public FastWriter write(char c)
  		{
  			return write((byte)c);
  		}
  
  		public FastWriter write(char[] s)
  		{
  			for(char c : s){
  				buf[ptr++] = (byte)c;
  				if(ptr == BUF_SIZE)innerflush();
  			}
  			return this;
  		}
  
  		public FastWriter write(String s)
  		{
  			s.chars().forEach(c -> {
  				buf[ptr++] = (byte)c;
  				if(ptr == BUF_SIZE)innerflush();
  			});
  			return this;
  		}
  
  		private static int countDigits(int l) {
  			if (l >= 1000000000) return 10;
  			if (l >= 100000000) return 9;
  			if (l >= 10000000) return 8;
  			if (l >= 1000000) return 7;
  			if (l >= 100000) return 6;
  			if (l >= 10000) return 5;
  			if (l >= 1000) return 4;
  			if (l >= 100) return 3;
  			if (l >= 10) return 2;
  			return 1;
  		}
  
  		public FastWriter write(int x)
  		{
  			if(x == Integer.MIN_VALUE){
  				return write((long)x);
  			}
  			if(ptr + 12 >= BUF_SIZE)innerflush();
  			if(x < 0){
  				write((byte)'-');
  				x = -x;
  			}
  			int d = countDigits(x);
  			for(int i = ptr + d - 1;i >= ptr;i--){
  				buf[i] = (byte)('0'+x%10);
  				x /= 10;
  			}
  			ptr += d;
  			return this;
  		}
  
  		private static int countDigits(long l) {
  			if (l >= 1000000000000000000L) return 19;
  			if (l >= 100000000000000000L) return 18;
  			if (l >= 10000000000000000L) return 17;
  			if (l >= 1000000000000000L) return 16;
  			if (l >= 100000000000000L) return 15;
  			if (l >= 10000000000000L) return 14;
  			if (l >= 1000000000000L) return 13;
  			if (l >= 100000000000L) return 12;
  			if (l >= 10000000000L) return 11;
  			if (l >= 1000000000L) return 10;
  			if (l >= 100000000L) return 9;
  			if (l >= 10000000L) return 8;
  			if (l >= 1000000L) return 7;
  			if (l >= 100000L) return 6;
  			if (l >= 10000L) return 5;
  			if (l >= 1000L) return 4;
  			if (l >= 100L) return 3;
  			if (l >= 10L) return 2;
  			return 1;
  		}
  
  		public FastWriter write(long x)
  		{
  			if(x == Long.MIN_VALUE){
  				return write("" + x);
  			}
  			if(ptr + 21 >= BUF_SIZE)innerflush();
  			if(x < 0){
  				write((byte)'-');
  				x = -x;
  			}
  			int d = countDigits(x);
  			for(int i = ptr + d - 1;i >= ptr;i--){
  				buf[i] = (byte)('0'+x%10);
  				x /= 10;
  			}
  			ptr += d;
  			return this;
  		}
  
  		public FastWriter write(double x, int precision)
  		{
  			if(x < 0){
  				write('-');
  				x = -x;
  			}
  			x += Math.pow(10, -precision)/2;
  			//		if(x < 0){ x = 0; }
  			write((long)x).write(".");
  			x -= (long)x;
  			for(int i = 0;i < precision;i++){
  				x *= 10;
  				write((char)('0'+(int)x));
  				x -= (int)x;
  			}
  			return this;
  		}
  
  		public FastWriter writeln(char c){
  			return write(c).writeln();
  		}
  
  		public FastWriter writeln(int x){
  			return write(x).writeln();
  		}
  
  		public FastWriter writeln(long x){
  			return write(x).writeln();
  		}
  
  		public FastWriter writeln(double x, int precision){
  			return write(x, precision).writeln();
  		}
  
  		public FastWriter write(int... xs)
  		{
  			boolean first = true;
  			for(int x : xs) {
  				if (!first) write(' ');
  				first = false;
  				write(x);
  			}
  			return this;
  		}
  
  		public FastWriter write(long... xs)
  		{
  			boolean first = true;
  			for(long x : xs) {
  				if (!first) write(' ');
  				first = false;
  				write(x);
  			}
  			return this;
  		}
  
  		public FastWriter writeln()
  		{
  			return write((byte)'\n');
  		}
  
  		public FastWriter writeln(int... xs)
  		{
  			return write(xs).writeln();
  		}
  
  		public FastWriter writeln(long... xs)
  		{
  			return write(xs).writeln();
  		}
  
  		public FastWriter writeln(char[] line)
  		{
  			return write(line).writeln();
  		}
  
  		public FastWriter writeln(char[]... map)
  		{
  			for(char[] line : map)write(line).writeln();
  			return this;
  		}
  
  		public FastWriter writeln(String s)
  		{
  			return write(s).writeln();
  		}
  
  		private void innerflush()
  		{
  			try {
  				out.write(buf, 0, ptr);
  				ptr = 0;
  			} catch (IOException e) {
  				throw new RuntimeException("innerflush");
  			}
  		}
  
  		public void flush()
  		{
  			innerflush();
  			try {
  				out.flush();
  			} catch (IOException e) {
  				throw new RuntimeException("flush");
  			}
  		}
  
  		public FastWriter print(byte b) { return write(b); }
  		public FastWriter print(char c) { return write(c); }
  		public FastWriter print(char[] s) { return write(s); }
  		public FastWriter print(String s) { return write(s); }
  		public FastWriter print(int x) { return write(x); }
  		public FastWriter print(long x) { return write(x); }
  		public FastWriter print(double x, int precision) { return write(x, precision); }
  		public FastWriter println(char c){ return writeln(c); }
  		public FastWriter println(int x){ return writeln(x); }
  		public FastWriter println(long x){ return writeln(x); }
  		public FastWriter println(double x, int precision){ return writeln(x, precision); }
  		public FastWriter print(int... xs) { return write(xs); }
  		public FastWriter print(long... xs) { return write(xs); }
  		public FastWriter println(int... xs) { return writeln(xs); }
  		public FastWriter println(long... xs) { return writeln(xs); }
  		public FastWriter println(char[] line) { return writeln(line); }
  		public FastWriter println(char[]... map) { return writeln(map); }
  		public FastWriter println(String s) { return writeln(s); }
  		public FastWriter println() { return writeln(); }
  	}
  
  	public void trnz(int... o)
  	{
  		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
  		System.out.println();
  	}
  
  	// print ids which are 1
  	public void trt(long... o)
  	{
  		Queue<Integer> stands = new ArrayDeque<>();
  		for(int i = 0;i < o.length;i++){
  			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
  		}
  		System.out.println(stands);
  	}
  
  	public void tf(boolean... r)
  	{
  		for(boolean x : r)System.out.print(x?'#':'.');
  		System.out.println();
  	}
  
  	public void tf(boolean[]... b)
  	{
  		for(boolean[] r : b) {
  			for(boolean x : r)System.out.print(x?'#':'.');
  			System.out.println();
  		}
  		System.out.println();
  	}
  
  	public void tf(long[]... b)
  	{
  		if(INPUT.length() != 0) {
  			for (long[] r : b) {
  				for (long x : r) {
  					for (int i = 0; i < 64; i++) {
  						System.out.print(x << ~i < 0 ? '#' : '.');
  					}
  				}
  				System.out.println();
  			}
  			System.out.println();
  		}
  	}
  
  	public void tf(long... b)
  	{
  		if(INPUT.length() != 0) {
  			for (long x : b) {
  				for (int i = 0; i < 64; i++) {
  					System.out.print(x << ~i < 0 ? '#' : '.');
  				}
  			}
  			System.out.println();
  		}
  	}
  
  	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
  	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
  }
  