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>

#define ll long long
#define ld long double
#define debug(x) \
	//    (cout << #x << ": " << (x) << endl)
#define eb emplace_back
#define fi first
#define se second

using namespace std;

const int nm = 3002;
const int mod = 998244353;

int n, m, a[nm];
int g[nm][nm];

int main() {
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
#endif
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; ++i) {
		scanf("%d", &a[i]);
	}
	g[0][0] = 1;
	for (int i = 1; i <= n; ++i) {
		g[i][0] = (g[i - 1][0] * 2) % mod;
		for (int j = 1; j <= m; ++j) {
			g[i][j] = (g[i - 1][j] * 2) % mod;
			if (a[i] <= j) {
				g[i][j] = (g[i][j] + g[i - 1][j - a[i]]) % mod;
			}
		}
	}
	printf("%d\n", g[n][m]);
}