Problem 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.

Constraints

• All values in input are integers.
• 1 \leq N \leq 3000
• 1 \leq S \leq 3000
• 1 \leq A_i \leq 3000

Sample Input 1

3 4
2 2 4

Sample Output 1

6

For each T, the value of f(T) is shown below. The sum of these values is 6.

• f(\{1\}) = 0
• f(\{2\}) = 0
• f(\{3\}) = 1 (One subset \{3\} satisfies the condition.)
• f(\{1, 2\}) = 1 (\{1, 2\})
• f(\{2, 3\}) = 1 (\{3\})
• f(\{1, 3\}) = 1 (\{3\})
• f(\{1, 2, 3\}) = 2 (\{1, 2\}, \{3\})

Sample Input 2

5 8
9 9 9 9 9

Sample Output 2

0

Sample Input 3

10 10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

3296