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>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

#define ll long long 
#define FI first 
#define SE second
#define pb push_back 
#define eb emplace_back
#define mod 998244353
#define all(c) (c).begin(),(c).end()
#define LB  lower_bound
#define UB  upper_bound
#define max3(a,b,c) max(c,max(a,b))
#define min3(a,b,c) min(c,min(a,b))
#define mems(s, n) memset(s, n, sizeof(s))
#define NINF -1e18
#define INF 1e18
#define int ll int
#define OOK order_of_key  //no of elements less than
#define FBO find_by_order //iterator pointing kth element;indexing starts from 0
#define CK3(x,y,z) cout<<(x)<<" "<<(y)<<" "<<(z)<<endl
#define CK4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<endl

typedef pair<int,int> PII;
typedef pair<pair<int,int>,int> PPII;
typedef pair<int,pair<int,int>> PIPI;
typedef map<int,int>MII;
typedef vector<int> VI;
template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

int power(int a, int b)
{int x=1,y=a;while(b>0){if(b%2){x =(x*y)%mod;}y =(y*y)%mod;b/=2;}return x%mod;}

int modInverse(int a, int m) {return power(a, m-2);} //gcd(a,m)=1 
int dp[3005][3005];bool vis[3005][3005];VI ar(3005);int n;
int solve(int i,int s)
{
    if(s==0)return power(2,n);
    if(i<0||s<0)return 0;
    if(vis[i][s]==false)
    {
        vis[i][s]=true;
        dp[i][s]=solve(i-1,s);
        
        dp[i][s]+=((solve(i-1,s-ar[i]))*modInverse(2,mod))%mod;
    }
    return dp[i][s];
}
signed main()
{
ios::sync_with_stdio(false); cin.tie(0);
int T=1,T1=0;//cin>>T;
while(T1++<T)
{
    int s;
    cin>>n>>s;
    for(int i=0;i<n;i++)cin>>ar[i];
    cout<<solve(n-1,s);
    
}


return 0;
}