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: Runtime Error)

#include<iostream>
#include<unordered_map>
#include<bitset>
#include<math.h>
#include<vector>
#include<set>
#include<algorithm>
#include<ctype.h>
#include<unordered_set>
#include<string>
#include<iomanip>
#include<queue>
#include<limits>
#include<map>
#include<stack>
#include<iterator>
#include<cstring>

#include<deque>
#define pi 3.141592653589793238
#include<chrono>

#define MOD 1000000007
#define INF 999999999999999999 
#define pb push_back
#define ff first
#define ss second
#define mt make_tuple
#define ll long long
#define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define f0 get<0>
#define f1 get<1>
#define f2 get<2>
#define db double
using namespace std;

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    fast;
    ll T = 1, i, j;
    
    //cin >> T;
    while (T--) {
        ll n, s;
        cin >> n >> s;
        vector<ll> v(n);
        for(i = 0 ; i < n ; i++){
            cin>> v[i];
        }
        ll mod = 998244353;
 
        ll dp[100][100] = { 0 };
        dp[0][0] = 1;
        for(i = 0 ; i < n; i++){
            for(j = 0; j <= s; j++){
                dp[i + 1][j] += 2 * dp[i][j];
            }
            for(j = v[i]; j <= s; j++){
                dp[i + 1][j] += dp[i][j - v[i]];
                dp[i + 1][j] %= mod;
            }
        }
        cout << dp[n][s];
    }
    
    return 0;
}