Lots of runners use personal Global Positioning System (GPS)
receivers to track how many miles they run. No GPS is perfect,
though: it only records its position periodically rather than
continuously, so it can miss parts of the true running path.
For this problem we’ll consider a GPS that works in the
following way when tracking a run:

At the beginning of the run, the GPS first records the
runner’s starting position at time $0$.

It then records the position every $t$ units of time.

It always records the position at the end of the run,
even if the total running time is not a multiple of
$t$.
The GPS assumes that the runner goes in a straight line
between each consecutive pair of recorded positions. Because of
this, a GPS can underestimate the total distance run.
For example, suppose someone runs in straight lines and at
constant speed between the positions on the left side of Table
1. The time they reach each position is shown next to the
position. They stopped running at time $11$. If the GPS records a position
every $2$ units of time,
its readings would be the records on the right side of Table
1.
Time

Position

Time

Position

$0$

$(0,0)$

$0$

$(0,0)$

$3$

$(0,3)$

$2$

$(0,2)$

$5$

$(2,5)$

$4$

$(1,4)$

$7$

$(0,7)$

$6$

$(1,6)$

$9$

$(2,5)$

$8$

$(1,6)$

$11$

$(0,3)$

$10$

$(1,4)$



$11$

$(0,3)$

Table 1: Actual Running Path on the left, GPS
readings on the right.
The total distance run is approximately $14.313708$ units, while the GPS
measures the distance as approximately $11.650281$ units. The difference
between the actual and GPS distance is approximately
$2.663427$ units, or
approximately $18.607525 \%
$ of the total run distance.
Given a sequence of positions and times for a running path,
as well as the GPS recording time interval $t$, calculate the percentage of the
total run distance that is lost by the GPS. Your computations
should assume that the runner goes at a constant speed in a
straight line between consecutive positions.
Input
The input consists of a single test case. The first line
contains two integers $n$
($2 \le n \le 100$) and
$t$ ($1 \le t \le 100$), where $n$ is the total number of positions
on the running path, and $t$ is the recording time interval of
the GPS (in seconds).
The next $n$ lines
contain three integers per line. The $i$th line has three integers
$x_ i$, $y_ i$ ($10^6 \le x_ i, y_ i \le 10^6$), and
$t_ i$ ($0 \le t_ i \le 10^6$), giving the
coordinates of the $i$th
position on the running path and the time (in seconds) that
position is reached. The values of $t_ i$’s are strictly increasing. The
first and last positions are the start and end of the run.
Thus, $t_1$ is always
zero.
It is guaranteed that the total run distance is greater than
zero.
Output
Output the percentage of the actual run distance that is
lost by the GPS. The answer is considered correct if it is
within $10^{5}$ of the
correct answer.
Sample Input 1 
Sample Output 1 
6 2
0 0 0
0 3 3
2 5 5
0 7 7
2 5 9
0 3 11

18.60752550117103
