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.

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.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 \dots A_N

Output

Print the answer.