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$A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S$.

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.

Input

Input is given from Standard Input in the following format:
N S
A_1 A_2 ... A_N

Output

Print the sum of f(T) 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

见题面 Input 部分

见题面 Output 部分