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;
typedef long long ll;
typedef pair<ll, ll> P;
const ll MOD = 998244353;
const ll INF = 1e18;
#define rep(i,m,n) for(ll i = (m); i <= (n); i++)
#define zep(i,m,n) for(ll i = (m); i < (n); i++)
#define rrep(i,m,n) for(ll i = (m); i >= (n); i--)
#define print(x) cout << (x) << endl;
#define printa(x,m,n) for(int i = (m); i <= n; i++){cout << (x[i]) << " ";} cout<<endl;

int main(){
	cin.tie(0); ios::sync_with_stdio(false);
	
	ll n, s; cin >> n >> s;
	ll a[n+1]; rep(i, 1, n)cin >> a[i];
	
	ll dp[n+1][s+1]; memset(dp, 0, sizeof(dp));
	dp[0][0] = 1;
	
	rep(i, 1, n){
		rep(j, 0, s){
			dp[i][j] += 2*dp[i-1][j]%MOD;
			dp[i][j] %= MOD;
		}
		
		rep(j, 0, s-a[i]){
			dp[i][j+a[i]] += dp[i-1][j];
			dp[i][j+a[i]] %= MOD;
		}
		
		//printa(dp[i], 0, s)
	}
	
	print(dp[n][s])
	
	return 0;
}