Walk

There is currently a grid of $ n \times m $. You have to walk start at $(1,k_1)(\forall 1\le k_1 \le m)$,end at $(n,k_2)(\forall 1\le k_2\le m)$.For every possible path, there will be a value $V$.The initial value of $V$ is $f[k_1]$ when you start at $(1,k_1)$.When you reach $(x,y)$, the value will become $V \times f [y]$.When you are located at $ (x, y) $ , you can walk to $ (x+1, P) (P \le y+S ( S (S (y)))) $

Where $S(x)=\lfloor log2(max(1,x))) \rfloor$

Calculate the sum of the value of all the ways module $998244353$.

Two ways $ A,B$ think different if $ \exists (x,y)$, $A$ passes $(x,y)$ but $B$ not.

The first line contains two integers $n,m$

The second line contains $m$ integers $f_1,f_2,...,f_m$

$1\le n,m\le 10^5,0 \le f_i\le 10^9$

print one integer — the answer to the problem.

5 4
1 2 3 4

7770

2022“杭电杯”中国大学生算法设计超级联赛（1）