output_description: For each dataset, output _p_ decimal values in same order as input. Write a
  blank line after that.
  
  You may output any number of digit and may contain an error less than 1.0e-6.
input_description: Input consists of several datasets.
  
  The first line of each dataset contains three integers _n_ , _m_ , _p_ , which
  means the number of nodes and edges of the graph, and the number of the
  children. Each node are numbered 0 to _n_ -1.
  
  Following _m_ lines contains information about edges. Each line has three
  integers. The first two integers means nodes on two endpoints of the edge. The
  third one is weight of the edge.
  
  Next _p_ lines represent _c_[_i_] respectively.
  
  Input terminates when _n_ = _m_ = _p_ = 0.
attempt: vertex, edge, children = (int(n) for n in input().split(" "))
  graph = []
  child = []
  for e in range(edge):
      graph.append([int(n) for n in input().split(" ")])
  for c in range(children):
      child.append(int(input()))
  print(1)
  
problem_description: H: Winter Bells
  
  The best night ever in the world has come! It's 8 p.m. of December 24th, yes,
  the night of Cristmas Eve. Santa Clause comes to a silent city with ringing
  bells. Overtaking north wind, from a sleigh a reindeer pulls she shoot
  presents to soxes hanged near windows for children.
  
  The sleigh she is on departs from a big christmas tree on the fringe of the
  city. Miracle power that the christmas tree spread over the sky like a web and
  form a paths that the sleigh can go on. Since the paths with thicker miracle
  power is easier to go, these paths can be expressed as undirected weighted
  graph.
  
  Derivering the present is very strict about time. When it begins dawning the
  miracle power rapidly weakens and Santa Clause can not continue derivering any
  more. Her pride as a Santa Clause never excuses such a thing, so she have to
  finish derivering before dawning.
  
  The sleigh a reindeer pulls departs from christmas tree (which corresponds to
  0th node), and go across the city to the opposite fringe (_n_ -1 th node)
  along the shortest path. Santa Clause create presents from the miracle power
  and shoot them from the sleigh the reindeer pulls at his full power. If there
  are two or more shortest paths, the reindeer selects one of all shortest paths
  with equal probability and go along it.
  
  By the way, in this city there are _p_ children that wish to see Santa Clause
  and are looking up the starlit sky from their home. Above the _i_ -th child's
  home there is a cross point of the miracle power that corresponds to
  _c_[_i_]-th node of the graph. The child can see Santa Clause if (and only if)
  Santa Clause go through the node.
  
  Please find the probability that each child can see Santa Clause.
samples: [{"input": "2 1\n    0 1 2\n    1 2 3\n    1\n    4 5 2\n    0 1 1\n    0 2 1\n    1 2 1\n    1 3 1\n    2 3 1\n    1\n    2\n    0 0 0", "output": ".00000000\n    \n    0.50000000\n    0.50000000"}]