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
#include <stdio.h>

const long long mod = 998244353;
const long long inv2 = (mod + 1) / 2;

int N, S; long long D[3030];

int main()
{
	scanf ("%d %d", &N, &S);
	
	D[0] = 1;
	for (int i = 0; i < N; i++) D[0] = D[0] * 2 % mod;
	
	while (N--){
		int x; scanf ("%d", &x);
		for (int i = S - x; i >= 0; i--){
			D[i + x] = (D[i + x] + D[i] * inv2) % mod;
		}
	}

	printf ("%lld\n", D[S]);

	return 0;
}
