K. Grammy's Kingdom
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

Grammy's kingdom is in danger. Some foreign invaders have intruded into her kingdom and they are destroying the traffic system. There are $$$n$$$ stations indexed from $$$1$$$ to $$$n$$$ in the traffic system. Moreover, there are $$$m$$$ ($$$m\leq n$$$) airports located in some of the stations. If you are in station $$$i$$$, you can transfer to station $$$i+1$$$ if $$$i$$$ and $$$i+1$$$ haven't been destroyed. If you are in station $$$i$$$ with an airport, you can fly to station $$$j$$$ if $$$i\leq j$$$ and station $$$j$$$ has an airport and both of the stations haven't been destroyed. We define the stability $$$G$$$ of the system as the number of routes that still available.

Formally, $$$G=\sum_{1\leq i\leq j\leq n}$$$[a person in station $$$i$$$ can transfer to station $$$j$$$ via several stations or airports].

At each moment $$$i$$$ ($$$1\leq i\leq n$$$), the invaders will randomly choose an undestroyed station $$$x$$$ and destroy it as well as the airport in it (If there exists an airport in it).

We define $$$E(x)$$$ as the expected value of $$$x$$$. Grammy wonders the value of $$$\sum_{i=1}^n E(G_i)$$$ modulo $$$998\,244\,353$$$. Could you please help her? Here, $$$G_i$$$ denotes the value of the stability $$$G$$$ after the invaders destroying the $$$i$$$-th chosen station at the $$$i$$$-th moment.

Input

The input contains only a single case.

The first line contains two positive integers $$$n$$$ and $$$m$$$ ($$$1\leq n\leq 2\,000\,000$$$, $$$0\leq m\leq n$$$), denoting the number of stations and the number of airports.

The second line contains $$$m$$$ distinct integers $$$x_1, x_2, \dots, x_m$$$ ($$$1\leq x_i\leq n$$$), denoting the indexes of station that has an airport.

Output

Output one integer, the value of $$$\sum_{i=1}^n E(G_i)$$$ modulo $$$998\,244\,353$$$.

Examples
Input
1 0
Output
0
Input
3 3
1 2 3
Output
4
Input
6 2
2 4
Output
16637434
Note

It can be proved that the answer can be represented as a rational number $$$\dfrac pq$$$ with $$$\gcd(p,q)=1$$$. Therefore, you are asked to find the value of $$$pq^{-1} \bmod 998\,244\,353$$$. It can be shown that $$$q \bmod 998\,244\,353\neq 0$$$ under the given constraints of the problem.