output_description: Print N lines. The i-th line should contain the expected value of the
  coordinate of the eventual position of rabbit i after K sets are performed.
  The output is considered correct if the absolute or relative error is at most
  10^{-9}.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N
      x_1 x_2 ... x_N
      M K
      a_1 a_2 ... a_M
attempt: import numpy as np
  
  n = int(input())
  x = list(map(int, input().split()))
  m, k = map(int, input().split())
  a = list(map(int, input().split()))
  b = []
  x2 = []
  c = []
  for i in range(1, n):
      b.append(i - 1)
      x2.append(x[i] - x[i - 1])
  for i in range(m):
      to = a[i] - 1
      b[to], b[to - 1] = b[to - 1], b[to]
  bai = np.zeros((n - 1, n - 1), dtype="int8")
  for i in range(n - 1):
      xx = b[i]
      bai[xx, i] = 1
  bai = np.mat(bai)
  bai = bai**k
  x2 = np.dot(x2, bai)
  x2 = np.array(x2)
  s = x[0]
  print(s)
  for i in x2[0]:
      s += i
      print(s)
  
problem_description: Statement
  
  There are N rabbits on a number line. The rabbits are conveniently numbered 1
  through N. The coordinate of the initial position of rabbit i is x_i.
  
  The rabbits will now take exercise on the number line, by performing _sets_
  described below. A set consists of M _jumps_. The j-th jump of a set is
  performed by rabbit a_j (2≤a_j≤N-1). For this jump, either rabbit a_j-1 or
  rabbit a_j+1 is chosen with equal probability (let the chosen rabbit be rabbit
  x), then rabbit a_j will jump to the symmetric point of its current position
  with respect to rabbit x.
  
  The rabbits will perform K sets in succession. For each rabbit, find the
  expected value of the coordinate of its eventual position after K sets are
  performed.
samples: [{"input": "3\n    -1 0 2\n    1 1\n    2", "output": "-1.0\n    1.0\n    2.0\n    \n\nRabbit 2 will perform the jump. If rabbit 1 is chosen, the coordinate of the\ndestination will be -2. If rabbit 3 is chosen, the coordinate of the\ndestination will be 4. Thus, the expected value of the coordinate of the\neventual position of rabbit 2 is 0.5\u00d7(-2)+0.5\u00d74=1.0.\n\n* * *"}, {"input": "3\n    1 -1 1\n    2 2\n    2 2", "output": "1.0\n    -1.0\n    1.0\n    \n\nx_i may not be distinct.\n\n* * *"}, {"input": "5\n    0 1 3 6 10\n    3 10\n    2 3 4", "output": "0.0\n    3.0\n    7.0\n    8.0\n    10.0"}]