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 = int(input())
  
  E = [[] for i in range(N + 1)]
  
  for i in range(N - 1):
      x, y = map(int, input().split())
      E[x].append(y)
      E[y].append(x)
  
  mod = 10**9 + 7
  
  from collections import deque
  
  Q = deque()
  
  USE = [0] * (N + 1)
  Q.append(1)
  H = [0] * (N + 1)
  H[1] = 1
  USE[1] = 1
  
  while Q:
      x = Q.pop()
      for to in E[x]:
          if USE[to] == 0:
              USE[to] = 1
              H[to] = H[x] + 1
              Q.append(to)
  
  EH = [(h, ind + 1) for ind, h in enumerate(H[1:])]
  EH.sort(reverse=True)
  
  COME = [1] * (N + 1)
  USE = [0] * (N + 1)
  
  for h, ind in EH:
      USE[ind] = 1
      for to in E[ind]:
          if USE[to] == 0:
              COME[to] += COME[ind]
  
  ANS = 0
  
  POW2 = [1]
  for i in range(N + 1):
      POW2.append(POW2[-1] * 2 % mod)
  
  for i in range(1, N + 1):
      SCORE = []
      for j in E[i]:
          if COME[j] < COME[i]:
              SCORE.append(COME[j])
  
      if sum(SCORE) < N - 1:
          SCORE.append(N - sum(SCORE) - 1)
  
      AV = 1
  
      for s in SCORE:
          AV += POW2[s] - 1
  
      ANS += POW2[N - 1] - AV
      # print(SCORE,AV)
  
  print((ANS * pow(POW2[N], mod - 2, mod)) % mod)
  
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"}]