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 Java (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;
public class Main {
	static ArrayList<Integer> allSubsets = new ArrayList<Integer>();
	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		int n = Integer.parseInt(st.nextToken());
 		int s = Integer.parseInt(st.nextToken());
 		int[] array = new int[n];
 		StringTokenizer st1 = new StringTokenizer(bf.readLine());
 		for(int i = 0;i<n;i++){
 			array[i] = Integer.parseInt(st1.nextToken());
 		}
 		long[][] dp = new long[n+1][s+1];
 		dp[0][0] = power(2, n, num)%num;
 		for(int i = 1;i<n;i++)
 			dp[0][i] = 0;
 		for(int i = 0;i<n;i++){
 			for(int j = 0;j<=s;j++){
 				dp[i+1][j]+= dp[i][j];
 				dp[i+1][j]%= num;
 				if (j+array[i] <=s){
 					dp[i+1][j+array[i]] += dp[i][j]*power(2, num-2, num);
 					dp[i+1][j+array[i]]%= num;
 				}
 			}
 			
 		}
 		out.println(dp[n][s]);
 		out.close();
 		
	}
	public static long power(long x, long y, long mod){
		long ans = 1;
		while(y>0){
			if (y%2==1)
				ans = (ans*x)%mod;
			x = (x*x)%mod;
			y/=2;
		}
		return ans;
	}

}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is