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 <bits/stdc++.h>
using namespace std;
const int P=998244353,MAXN=3010;
int n,s,x,dp[MAXN],inv2;
int main () {
	inv2=(P+1)/2;
	scanf("%d%d",&n,&s);
	dp[0]=1;
	for (int i=1;i<=n;i++) {dp[0]=(1ll*dp[0]*2)%P;}
	for (int i=1;i<=n;i++) {
		scanf("%d",&x);
		for (int i=s-x;i>=0;i--) {
			dp[i+x]=(dp[i+x]+(1ll*dp[i]*inv2)%P)%P;
		}
	}
	printf("%d\n",dp[s]);
	return 0;
}