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: Wrong Answer)

#include <stdbool.h>
#include <stdio.h>
typedef long long ll;
#define MOD 998244353
int n, s, a[3000];
ll cnt = 0;
ll ans = 0;
ll modpow(ll a, ll n) {
	if (n == 0)
		return 1;
	if (n == 1)
		return (a % MOD);
	if (n % 2 == 1)
		return (a * modpow(a, n - 1) % MOD);
	ll t = modpow(a, n / 2);
	return (t * t % MOD);
}
void dfs(int cn, int sum, bool choice) {
	if (sum >= s || cn == n) {
		if (sum == s) {
			ans += modpow(2, n - cnt);
			ans %= MOD;
			cnt = 0;
		}
		return;
	}
	for (int i = 0; i < 2; i++) {
		int ts = sum;
		if (choice) {
			ts += a[cn];
			cnt++;
		}
		dfs(cn + 1, ts, i);
	}
	return;
}
int main() {
	scanf("%d%d", &n, &s);
	for (int i = 0; i < n; i++) {
		scanf("%d", &a[i]);
	}
	for (int i = 0; i < 2; i++) {
		dfs(0, 0, i);
	}
	printf("%lld\n", ans);
	return 0;
}