Problem Statement

You are given a set $S = \lbrace s_1,s_2,\dots,s_M \rbrace$ of non-negative integers between $0$ and $2^N - 1$ (inclusive).

You start with a non-negative integer $x = 0$. Find the number, modulo $998244353$, of ways to reach $x = 2^N$ by performing the following operation any number of times:

• Choose an integer $i$ with $1 \le i \le M$, and replace $x$ with $(x\ \mathrm{OR}\ s_i) + 1$.

Here, $\mathrm{OR}$ denotes the bitwise logical OR.

Constraints

• $1 \le N \le 24$
• $1 \le M \le \min(2^N,2 \times 10^{5})$
• $0 \le s_1 < s_2 < \dots < s_M < 2^N$

Input

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

N M
s_1\ s_2\ \dots\ s_M

Output

Output the number of ways, modulo $998244353$.