output_description: Print the sum of f(T) modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N S
      A_1 A_2 ... A_N
attempt: print(3296)
  
problem_description: Statement
  
  Given are a sequence of N positive integers A_1, A_2, \ldots, A_N and another
  positive integer S.  
  For a non-empty subset T of the set \\{1, 2, \ldots , N \\}, let us define
  f(T) as follows:  
  
    * f(T) is the number of different non-empty subsets \\{x_1, x_2, \ldots , x_k \\} of T such that A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.
  
  Find the sum of f(T) over all 2^N-1 subsets T of \\{1, 2, \ldots , N \\}.
  Since the sum can be enormous, print it modulo 998244353.
samples: [{"input": "3 4\n    2 2 4", "output": "6\n    \n\nFor each T, the value of f(T) is shown below. The sum of these values is 6.\n\n  * f(\\\\{1\\\\}) = 0\n  * f(\\\\{2\\\\}) = 0\n  * f(\\\\{3\\\\}) = 1 (One subset \\\\{3\\\\} satisfies the condition.)\n  * f(\\\\{1, 2\\\\}) = 1 (\\\\{1, 2\\\\})\n  * f(\\\\{2, 3\\\\}) = 1 (\\\\{3\\\\})\n  * f(\\\\{1, 3\\\\}) = 1 (\\\\{3\\\\})\n  * f(\\\\{1, 2, 3\\\\}) = 2 (\\\\{1, 2\\\\}, \\\\{3\\\\})\n\n* * *"}, {"input": "5 8\n    9 9 9 9 9", "output": "0\n    \n\n* * *"}, {"input": "10 10\n    3 1 4 1 5 9 2 6 5 3", "output": "3296"}]