Problem Statement

There is a length-$N$ sequence $B=(B_1,B_2,\ldots,B_N)$ consisting of $0$ and $1$. Initially, $B_1=1$, and all other elements are $0$.

There are $M$ switches, and the integer $A_i$ is written on switch $i$ ($1 \le i \le M$). When switch $i$ is pressed, using the state immediately before the operation, $B_j$ is simultaneously changed as follows for every integer $j$ satisfying $1 \le j \le N$:

[ B_j \leftarrow \begin{cases} B_j \oplus B_{j-A_i} & (A_i \lt j),\ B_j & (j \le A_i) \end{cases} ]

Each switch can be pressed zero times or once, and the switches may be pressed in any order.

Find the number, modulo $998244353$, of possible final sequences $B$.

What is the bitwise $\mathrm{XOR}$ operation? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, denoted $A \oplus B$, is defined as follows: The digit in the $2^k$'s place ($k \geq 0$) of $A \oplus B$, written in binary, is $1$ if exactly one of the digits in the $2^k$'s place of $A$ and $B$, written in binary, is $1$, and $0$ otherwise. For example, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$). In general, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$, and it can be proved that this does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $2 \le N \le 2 \times 10^5$
• $1 \le M \le 2 \times 10^5$
• $1 \le A_i \lt N$ ($1 \le i \le M$)
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 \ldots A_M

Output

Output the number, modulo $998244353$, of possible final sequences $B$.