Problem: Mr. Scrooge, a very busy man, decided to count the time he wastes on all sorts of useless stuff to evaluate the lost profit. He has already counted the time he wastes sleeping and eating. And now Mr. Scrooge wants to count the time he has wasted signing papers.

Mr. Scrooge's signature can be represented as a polyline A1A2... An. Scrooge signs like that: first it places a pen at the point A1, then draws a segment from point A1 to point A2, then he draws a segment from point A2 to point A3 and so on to point An, where he stops signing and takes the pen off the paper. At that the resulting line can intersect with itself and partially repeat itself but Scrooge pays no attention to it and never changes his signing style. As Scrooge makes the signature, he never takes the pen off the paper and his writing speed is constant — 50 millimeters per second.

Scrooge signed exactly k papers throughout his life and all those signatures look the same.

Find the total time Scrooge wasted signing the papers.

Input

The first line contains two integers n and k (2 ≤ n ≤ 100, 1 ≤ k ≤ 1000). Each of the following n lines contains the coordinates of the polyline's endpoints. The i-th one contains coordinates of the point Ai — integers xi and yi, separated by a space.

All points Ai are different. The absolute value of all coordinates does not exceed 20. The coordinates are measured in millimeters.

Output

Print one real number — the total time Scrooges wastes on signing the papers in seconds. The absolute or relative error should not exceed 10 - 6.

Examples

Input

2 1
0 0
10 0


Output

0.200000000

Input

5 10
3 1
-5 6
-2 -1
3 2
10 0


Output

6.032163204

Input

6 10
5 0
4 0
6 0
3 0
7 0
2 0


Output

3.000000000

Solution (in JAVA):

Solution:
//*******************************************************************
// Welcome to CompileJava!
// If you experience any issues, please contact us ('More Info')  -->
//*******************************************************************

import java.util.*;
import java.io.*;
public class Main {
public static void main(String[] args) throws IOException {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st = new StringTokenizer(br.readLine());

int n = Integer.parseInt(st.nextToken());
int k = Integer.parseInt(st.nextToken());
double sigDist = 0.0;

st = new StringTokenizer(br.readLine());
int a = Integer.parseInt(st.nextToken());
int b = Integer.parseInt(st.nextToken());

for (int i = 0; i < n-1; i++) {
	st = new StringTokenizer(br.readLine());
	int c = Integer.parseInt(st.nextToken());
	int d = Integer.parseInt(st.nextToken());
	sigDist += getDist(a, b, c, d);
	a = c;
	b = d;	
}
System.out.println(sigDist * k / 50.0); 
}

private static double getDist(int x1, int y1, int x2, int y2) {
	return Math.sqrt(Math.pow(x2-x1, 2) + Math.pow(y2-y1, 2)); 
}
} 

/*
import java.lang.Math; // headers MUST be above the first class

// one class needs to have a main() method
public css HelloWorld
{
  // arguments are passed using the text field below this editor
  {
    OtherClass myObject = new OtherClass("Hello World!");
    System.out.print(myObject);
  }
}
 you can add other public classes to this editor in any order
public lass OtherClass
{
  private String message;
  private boolean answer = false;
  public OtherClass(String input)
  {
    message = "Why, " + input + " Isn't this something?";
  }
  public String toString()
  {
    return message;
  }
}
*/