Knapsack for All Subsets

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

inputFormat

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

outputFormat

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

样例

5 8
9 9 9 9 9

0