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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Console;
using static System.Math;

class MainClass
{
    static readonly long mod = 998244353;
    static void Main()
    {
        var NS = ReadLine().Split().Select(int.Parse).ToArray();
        int N = NS[0];
        int S = NS[1];
        var A = ReadLine().Split().Select(int.Parse).ToArray();

        var dp = new BigInteger[N+1][];
        for (int i = 0; i < N+1; i++)
        {
            dp[i] = new BigInteger[S + 1];
            
        }

        dp[0][0] = (1 << N);

        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < S+1; j++)
            {
                dp[i + 1][j] += dp[i][j];
                if ((long)dp[i][j] > 0)
                {
                    int k = j + A[i];
                    if (k > S) continue;
                    
                    dp[i + 1][k] += dp[i][j] / 2;
                }
            }
        }
        WriteLine((long)dp[N][S]%mod);
    }
}