output_description: Print the number of the sets of bowls of ramen that satisfy the conditions,
  disregarding order, modulo M.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M
attempt: import sys
  
  input = sys.stdin.readline
  import numpy as np
  
  N, MOD = map(int, input().split())
  
  """
  余事象を調べる。包除の原理を使う。
  A[n] = （1,2,...,n）が1杯以下、他は何でも良い
  B[n,l] : (1,2,...,n) をlグループに分ける方法の個数
  A[n]
  ・0杯のグループあり
  ・なし
  """
  
  B = np.zeros((N + 1, N + 1), dtype=np.int64)
  B[0, 0] = 1
  for n in range(1, N + 1):
      # 1番を単独で使う
      B[n, 1:] = B[n - 1, :-1]
      # 1番をどこかに混ぜてもらう
      B[n, 1:] += B[n - 1, 1:] * np.arange(1, N + 1) % MOD
      B[n] %= MOD
  
  # 2^{kl}
  pow_2 = np.ones((N + 1, N + 1), dtype=np.int64)
  for n in range(1, N + 1):
      pow_2[1, n] = 2 * pow_2[1, n - 1] % MOD
  for n in range(2, N + 1):
      pow_2[n] = pow_2[n - 1] * pow_2[1] % MOD
  
  A = np.zeros(N + 1, dtype=np.int64)
  for n in range(N + 1):
      A[n] = (
          pow(2, pow(2, N - n, MOD - 1), MOD)
          * B[n, 1:]
          % MOD
          * (pow_2[N - n, 1:] + pow_2[N - n, :-1] * np.arange(1, N + 1) % MOD)
          % MOD
      ).sum() % MOD
  
  comb = np.zeros((N + 1, N + 1), dtype=np.int64)
  comb[:, 0] = 1
  for n in range(1, N + 1):
      comb[n, 1:] = (comb[n - 1, 1:] + comb[n - 1, :-1]) % MOD
  
  A[::2] *= -1
  A *= comb[N]
  answer = pow(2, pow(2, N, MOD - 1), MOD) - A.sum()
  answer %= MOD
  print(answer)
  
problem_description: Statement
  
  In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen",
  but N kinds of toppings are also offered. When a customer orders a bowl of
  ramen, for each kind of topping, he/she can choose whether to put it on top of
  his/her ramen or not. There is no limit on the number of toppings, and it is
  allowed to have all kinds of toppings or no topping at all. That is,
  considering the combination of the toppings, 2^N types of ramen can be
  ordered.
  
  Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen
  that satisfy both of the following two conditions:
  
    * Do not order multiple bowls of ramen with the exactly same set of toppings.
    * Each of the N kinds of toppings is on two or more bowls of ramen ordered.
  
  You are given N and a prime number M. Find the number of the sets of bowls of
  ramen that satisfy these conditions, disregarding order, modulo M. Since she
  is in extreme hunger, ordering any number of bowls of ramen is fine.
samples: [{"input": "2 1000000007", "output": "2\n    \n\nLet the two kinds of toppings be A and B. Four types of ramen can be ordered:\n\"no toppings\", \"with A\", \"with B\" and \"with A, B\". There are two sets of ramen\nthat satisfy the conditions:\n\n  * The following three ramen: \"with A\", \"with B\", \"with A, B\".\n  * Four ramen, one for each type.\n\n* * *"}, {"input": "3 1000000009", "output": "118\n    \n\nLet the three kinds of toppings be A, B and C. In addition to the four types\nof ramen above, four more types of ramen can be ordered, where C is added to\nthe above four. There are 118 sets of ramen that satisfy the conditions, and\nhere are some of them:\n\n  * The following three ramen: \"with A, B\", \"with A, C\", \"with B, C\".\n  * The following five ramen: \"no toppings\", \"with A\", \"with A, B\", \"with B, C\", \"with A, B, C\".\n  * Eight ramen, one for each type.\n\nNote that the set of the following three does not satisfy the condition:\n\"'with A', 'with B', 'with A, B'\", because C is not on any of them.\n\n* * *"}, {"input": "50 111111113", "output": "1456748\n    \n\nRemember to print the number of the sets modulo M. Note that these three\nsample inputs above are included in the test set for the partial score.\n\n* * *"}, {"input": "3000 123456791", "output": "16369789\n    \n\nThis sample input is not included in the test set for the partial score."}]