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
  
  if N < K:
      print(0)
  else:
      ans = 0
      v = 1
      for i in range(K):
          if i % 2:
              ans -= pow(K - i, N, MOD) * v
          else:
              ans += pow(K - i, N, MOD) * v
          v = v * (K - i) * pow(i + 1, MOD - 2, MOD) % MOD
      print(ans % 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 distinguished from the other.
    * Each box is 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": "4 3", "output": "36"}, {"input": "10 3", "output": "55980"}, {"input": "100 100", "output": "437918130"}]