output_description: Print the answer.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
      a_1 a_2 \ldots a_K
attempt: P = 10**9 + 7
  fa = [1]
  for i in range(1, 1010):
      fa.append(fa[-1] * i % P)
  fainv = [pow(fa[-1], P - 2, P)]
  for i in range(1, 1010)[::-1]:
      fainv.append(fainv[-1] * i % P)
  fainv = fainv[::-1]
  
  k = 70
  kk = 1 << k
  nu = lambda L: int("".join([bin(kk + a)[-k:] for a in L[::-1]]), 2)
  st = lambda n: bin(n)[2:] + "0"
  li = lambda s: [
      int(a, 2) % P if len(a) else 0
      for a in [s[-(i + 1) * k - 1 : -i * k - 1] for i in range(N + 1)]
  ]
  
  N, K = map(int, input().split())
  A = [int(a) for a in input().split()]
  X = [fa[N]] + [0] * N
  for a in A:
      X = li(
          st(
              nu(X)
              * nu(
                  [
                      (
                          fainv[i] * fa[N - i] * fainv[a - i] * fainv[N - a] % P
                          if i <= a
                          else 0
                      )
                      for i in range(N + 1)
                  ]
              )
          )
      )
  
  print(X[-1])
  
problem_description: Statement
  
  There are N children, numbered 1,2,\ldots,N. In the next K days, we will give
  them some cookies. In the i-th day, we will choose a_i children among the N
  with equal probability, and give one cookie to each child chosen. (We make
  these K choices independently.)
  
  Let us define the _happiness_ of the children as c_1 \times c_2 \times \ldots
  \times c_N, where c_i is the number of cookies received by Child i in the K
  days. Find the expected happiness multiplied by \binom{N}{a_1} \times
  \binom{N}{a_2} \times \ldots \times \binom{N}{a_K} (we can show that this
  value is an integer), modulo (10^{9}+7).
samples: [{"input": "3 2\n    3 2", "output": "12\n    \n\n  * On the first day, all the children 1, 2, and 3 receive one cookie.\n  * On the second day, two out of the three children 1, 2, and 3 receive one cookie.\n  * Their happiness is 4 in any case, so the expected happiness is 4. Print this value multiplied by \\binom{3}{3} \\times \\binom{3}{2}, which is 12.\n\n* * *"}, {"input": "856 16\n    399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63", "output": "337587117\n    \n\n  * Find the expected value multiplied by \\binom{N}{a_1} \\times \\binom{N}{a_2} \\times \\ldots \\times \\binom{N}{a_K}, modulo (10^9+7)."}]