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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int f[3001][3001],p[3001],ans=0;
int n,a[3001],s,mod=998244353;
int main(){
	cin>>n>>s;
	int i,j,k;
	p[0]=1;
	for(i=1;i<=n;++i)cin>>a[i],p[i]=p[i-1]*2%mod;
	f[0][0]=1;
	for(i=1;i<=n;++i){
		for(j=i;j;--j){
			for(k=a[i];k<=s;++k){
				f[j][k]+=f[j-1][k-a[i]];
				//cout<<i<<" "<<j<<" "<<k<<" "<<f[j][k]<<endl;
			}
		}
	}
	for(i=1;i<=n;++i){
		//cout<<f[i][s]<<endl;
		ans+=f[i][s]*p[n-i]%mod;
		ans%=mod;
	}
	cout<<ans;
}