# Journey

Recent inquiries of the Ministry of Transport of Flatland proved that when a flatmobile travels through the land, it spends energy not only for moving, but also for turning. More exactly, if a flatmobile’s path is a polyline, the total amount of energy spent is the sum of the total length of the polyline and the energy losses at the turn points, excluding the starting and the ending point. The energy loss at a turn point is the angle by which the polyline turns at the point multiplied by a factor k. Angles are counted in degrees. Flatland has N cities connected by M one-way roads. Each road is a straight line. You decided to make a journey from one city to another. Your flatmobile can travel only using the roads. You want to find a path with minimal energy consumption. Input The first line of the input contains the number of the test cases, which is at most 15. The descriptions of the test cases follow. The first line of a test case description contains four integers N, M, S, and F (1 ≤ N ≤ 1000,0 ≤ M ≤ 10000,1 ≤ S,F ≤ N) and a number k (0.00001 ≤ k ≤ 10) separated by spaces. S and F are your start and finish cities respectively; S ̸= F . Each of the next N lines contains two integers X and Y (−10000 ≤ X, Y ≤ 10000) separated by space, being the coordinates of a city. The i + 1-st line contains the coordinates of city i. No two cities are in the same point. Each of the next M lines contains two integers, A and B (1 ≤ A, B ≤ N, A ≤ B) separated by a space, representing a road from city A to city B. For any two cities, there is at most one road going from one city to the other. Each city has at most ten roads going from it. The cities are numbered starting from 1. The test cases are separated by blank lines. Output For each test case in the input, output the minimal possible energy consumption with at least three digits after the decimal point, or ‘Impossible’ (without quotes), if there is no way from S to F over the roads. If there is a way, the second line of the output file must contain the numbers of the cities on the optimal path starting from S and finishing at F . If there are several optimal solutions, output any of them. Print a blank line between test cases. Sample Input 2 5 5 1 3 0.01 00 4 -4 80 41 4 -1 12 14 23 53 45

2/2 20121 00 11 Sample Output 12.214 123 Impossible