output_description: Print the number of ways modulo $10^9+7$ in a line.
input_description: $n$ $k$
      
  
  The first line will contain two integers $n$ and $k$.
attempt: N, K = map(int, input().split())
  MOD = 10**9 + 7
  
  D = [[0] * (K + 1) for i in range(N + 1)]
  for i in range(1, N + 1):
      D[i][1] = 1
  for i in range(1, min(N, K) + 1):
      D[i][i] = 1
  for n in range(1, N + 1):
      for k in range(2, min(n - 1, K) + 1):
          D[n][k] = (D[n - k][k] + D[n - 1][k - 1]) % MOD
  print(D[N][K] % MOD)
  
problem_description: You have $n$ balls and $k$ boxes. You want to put these balls into the boxes.
  
  Find the number of ways to put the balls under the following conditions:
  
    * Each ball is **not** distinguished from the other.
    * Each box is **not** distinguished from the other.
    * Each ball can go into only one box and no one remains outside of the boxes.
    * Each box must contain at least one ball.
  
  Note that you must print this count modulo $10^9+7$.
samples: [{"input": "10 5", "output": "7"}, {"input": "30 15", "output": "176"}, {"input": "100 30", "output": "3910071"}]