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