8483: Walk

There is currently a grid of n × m. You have to walk start at (1,k 1 )(∀1 ≤ k 1 ≤ m),end at
(n,k 2 )(∀1 ≤ k 2 ≤ 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 ×f[y].When you are located at
(x,y) , you can walk to (x + 1,P)(P ≤ y + S(S(S(y))))
Where S(x) = blog2(max(1,x)))c
Calculate the sum of the value of all the ways module 998244353.
Two ways A,B think different if ∃(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 ≤ n,m ≤ 10 5 ,0 ≤ f i ≤ 10 9

print one integer — the answer to the problem.