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: mod = 10**9 + 7
  M = 1000
  
  fact = [1] * (M + 1)
  factinv = [1] * (M + 1)
  inv = [1] * (M + 1)
  for n in range(2, M + 1):
      fact[n] = n * fact[n - 1] % mod
      inv[n] = -inv[mod % n] * (mod // n) % mod
      factinv[n] = inv[n] * factinv[n - 1] % mod
  
  
  def comb(n, k):
      return fact[n] * factinv[k] * factinv[n - k] % mod
  
  
  N, K = map(int, input().split())
  a = list(map(int, input().split()))
  
  dp = [[0] * (N + 1) for i in range(K + 1)]
  dp[0][0] = 1
  
  for k in range(K):
      for n in range(1, N + 1):
          for i in range(min(a[k] + 1, n + 1)):
              dp[k + 1][n] += (
                  fact[a[k]]
                  * factinv[a[k] - i]
                  * fact[N - i]
                  * factinv[N]
                  * comb(n, i)
                  * dp[k][n - i]
              )
              dp[k + 1][n] %= mod
  ans = dp[-1][-1]
  for i in range(K):
      ans *= comb(N, a[i])
      ans %= mod
  
  print(ans)
  
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)."}]