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.

Examples

Input

3 4
2 2 4


Output

6


Input

5 8
9 9 9 9 9


Output

0


Input

10 10
3 1 4 1 5 9 2 6 5 3


Output

3296
import java.util.*;
import java.io.*;
public class Main {
	static int num = 998244353;
	public static void main(String[] args) throws Exception{
		

		// 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());
 		long mult = power(2, num-2, num);
 		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<=s;i++)
 			dp[0][i] = (long)(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]*mult;
 					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%num;
	}

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

 		
 		
 		
 		
	


