15428 번 : Imperfect GPS 
 15428 번 
 15428 번 - Imperfect GPS 스페셜 저지 
 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 . 
 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 . 
 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 ) 
 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 . 
 The input consists of a single test case . The first line contains two integers n ( 2 ≤ n ≤ 100 ) and t ( 1 ≤ t ≤ 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 xi , yi ( − 106 ≤ xi , yi ≤ 106 ) , and ti ( 0 ≤ ti ≤ 106 ) , giving the coordinates of the i - th position on the running path and the time ( in seconds ) that position is reached . The values of ti ’ s are strictly increasing . The first and last positions are the start and end of the run . Thus , t 1 is always zero . 
 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 . 
 ACM - ICPC > Regionals > North America > North America Qualification Contest > ACM - ICPC North America Qualifier 2017 H 번