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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
 
using namespace std;

const long long int MOD = 998244353;
long long int dp[3001][3001];
vector <int> A;
int n,s,t;

int main(void)
{
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> n >> s;
	for(int i=0;i<n;i++)
	{
		cin >> t;
		A.push_back(t);
	}

	dp[0][0] = 1;
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<=s;j++)
		{
			dp[i+1][j] = ((dp[i+1][j]%MOD) + ((2*dp[i][j])%MOD));
			dp[i+1][j]%=MOD;
			if(j + A[i] <= s)
			{
				dp[i+1][j+A[i]] = ((dp[i+1][j+A[i]]%MOD) + (dp[i][j]%MOD)%MOD);
				dp[i+1][j+A[i]]%=MOD;
			}
		}
	}

	cout << dp[n][s] << '\n';
	
    return 0;
}