output_description: Print the expected holeyness of S, \bmod 10^9+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_1 B_1
      :
      A_{N-1} B_{N-1}
attempt: n, m = map(int, input().split())
  a = list(map(int, input().split()))
  
  a.sort()
  lr = []
  
  
  for ai in a[: m // 2]:
      for aj in a[: m // 2]:
          lr.append(ai + aj)
  lr.sort()
  
  print(sum(lr[-m:]))
  
problem_description: Statement
  
  Given is a tree T with N vertices. The i-th edge connects Vertex A_i and B_i
  (1 \leq A_i,B_i \leq N).
  
  Now, each vertex is painted black with probability 1/2 and white with
  probability 1/2, which is chosen independently from other vertices. Then, let
  S be the smallest subtree (connected subgraph) of T containing all the
  vertices painted black. (If no vertex is painted black, S is the empty graph.)
  
  Let the _holeyness_ of S be the number of white vertices contained in S. Find
  the expected holeyness of S.
  
  Since the answer is a rational number, we ask you to print it \bmod 10^9+7, as
  described in Notes.
samples: [{"input": "3\n    1 2\n    2 3", "output": "125000001\n    \n\nIf the vertices 1, 2, 3 are painted black, white, black, respectively, the\nholeyness of S is 1.\n\nOtherwise, the holeyness is 0, so the expected holeyness is 1/8.\n\nSince 8 \\times 125000001 \\equiv 1 \\pmod{10^9+7}, we should print 125000001.\n\n* * *"}, {"input": "4\n    1 2\n    2 3\n    3 4", "output": "375000003\n    \n\nThe expected holeyness is 3/8.\n\nSince 8 \\times 375000003 \\equiv 3 \\pmod{10^9+7}, we should print 375000003.\n\n* * *"}, {"input": "4\n    1 2\n    1 3\n    1 4", "output": "250000002\n    \n\nThe expected holeyness is 1/4.\n\n* * *"}, {"input": "7\n    4 7\n    3 1\n    2 6\n    5 2\n    7 1\n    2 7", "output": "570312505"}]