output_description: Print T lines. The i-th line should contain the answer to the i-th test case.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      T
      \mathrm{case}_1
      \vdots
      \mathrm{case}_T
      
  
  Each case is given in the following format:
  
      
      
      N
attempt: import numpy as np
  
  conv = np.convolve
  
  
  def beki(P, Q, n):
      while n:
          Q1 = Q.copy()
          Q1[1::2] = -Q[1::2]
  
          P = conv(P, Q1)[n & 1 :: 2]
          Q = conv(Q, Q1)[::2]
          n >>= 1
      return P[0]
  
  
  mod = 10**9 + 7
  t = int(input())
  p = [0, 0, 0, 0, 0, 1]
  q = [1]
  for _ in range(16):
      q = conv(q, [-1, 1])
  for _ in range(5):
      q = conv(q, [1, 1])
  for i in range(t):
      n = int(input())
      print(beki(p, q, n) % mod)
  
problem_description: Statement
  
  Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1,
  u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will
  be satisfied:
  
    * 0 \leq s_1 < s_2
    * 0 \leq n_1 < n_2
    * 0 \leq u_1 < u_2
    * 0 \leq k_1 < k_2
    * 0 \leq e_1 < e_2
    * s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
  
  For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute
  (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of
  all computed values, modulo (10^{9} +7).
  
  Solve this problem for each of the T test cases given.
samples: [{"input": "4\n    4\n    6\n    10\n    1000000000", "output": "0\n    11\n    4598\n    257255556\n    \n\n  * When N=4, there is no possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2). Thus, the answer is 0.\n  * When N=6, there are six possible choices (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2) as follows:\n    * (0,1,0,1,0,1,0,1,0,1)\n    * (0,2,0,1,0,1,0,1,0,1)\n    * (0,1,0,2,0,1,0,1,0,1)\n    * (0,1,0,1,0,2,0,1,0,1)\n    * (0,1,0,1,0,1,0,2,0,1)\n    * (0,1,0,1,0,1,0,1,0,2)\n  * We have one choice where (s_2 \u2212 s_1)(n_2 \u2212 n_1)(u_2 \u2212 u_1)(k_2 - k_1)(e_2 - e_1) is 1 and five choices where (s_2 \u2212 s_1)(n_2 \u2212 n_1)(u_2 \u2212 u_1)(k_2 - k_1)(e_2 - e_1) is 2, so the answer is 11.\n  * Be sure to find the sum modulo (10^{9} +7)."}]