Problem:
Score : 600 points

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

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.

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

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n, s = map(int, input().split())
a = list(map(int, input().split()))

mod = 998244353

pows = [1]
for i in range(10000):
    pows.append((pows[-1] * 2) % mod)

dp = [0] * (s + 1)
dp[0] = 1
if a[0] <= s:
    dp[a[0]] = 1

for i in range(1, n):
    dp_new = [0] * (s + 1)
    dp_new[0] = 1
    for j in range(1, s + 1):
        dp_new[j] = dp[j] * 2

        if j - a[i-1] > 0:
            dp_new[j] += dp[j-a[i-1]]
        elif j == a[i-1]:
            dp_new[j] += pows[i]
        dp_new[j] %= mod

    dp = dp_new

print(dp[-1])