Problem Statement

You are given $a sequence A=(A_1,A_2,\dots,A_N)$ of length N.
Find the number, modulo 998244353, of ways to choose an odd number of elements from A so that the sum of the chosen elements equals M.
Two choices are said to be different if there exists an integer $i (1 \le i \le N)$ such that one chooses A_i but the other does not.

Input

Input is given from Standard Input in the following format:
N M
$A_1 A_2 \dots A_N$

Output

Print the answer.

Constraints

• $1 \le N \le 10^5$
• $1 \le M \le 10^6$
• $1 \le A_i \le 10$
• All values in input are integers.

Sample Input 1

5 6
1 2 3 3 6

Sample Output 1

3

The following 3 choices satisfy the condition:

• Choosing A_1, A_2, and A_3.
• Choosing A_1, A_2, and A_4.
• Choosing A_5.

Choosing A_3 and A_4 does not satisfy the condition because, although the sum is 6, the number of chosen elements is not odd.

Sample Input 2

10 23
1 2 3 4 5 6 7 8 9 10

Sample Output 2

18

见题面 Input 部分

见题面 Output 部分