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 $998244353$.