Problem Description

Define $F(k, n)$ as follows:

$$F(k,n) = \left \{ \begin{aligned} &st_0\ && k = 1\ \land\ n = 0 \\ &st_1\ && k = 1\ \land\ n = 1 \\ &0\ && k > 1 \ \land \ n < 0 \\ &a \times F(k, n - 1) + b \times F(k, n - 2)\ && k = 1 \ \land\ n > 1 \\ &t_k \times F(k, n - 1) + s^n \times F(k - 1, n)\ && \text{otherwise} \end{aligned} \right.$$

Given the coefficients in the recurrence of $F$ and $k, n$, compute the value of $F(k, n) \bmod 998244353$.

Input Format

The first line contains two integers $k, n$.

The second line contains five integers $st_0, st_1, a, b, s$.

The third line contains $k - 1$ integers $t_2, t_3, \cdots, t_k$.

Output Format

Output one integer on a single line, which is the answer.

10 25
-5 -73 -95 64 15
-80 -31 -58 15 95 -1 14 -30 31 

998096342

Hint

$\textbf{Subtask}$	$k \leq$	$n \leq$	Special Property	Score
$1$	$100$	$100$	None	$5$
$2$		$2^{63}$		$25$
$3$	$5000$		$s = 1, \forall 2 \leq i \leq k, t_i = 1$	$10$
$4$			None	$60$

For $100\%$ of the testdata, $1 \leq k \leq 5 \times 10^3$, $0 \leq n \le 2^{63}$, and $-998244352 \leq st_0, st_1, a, b, s, t_i \leq 998244352$.

Translated by ChatGPT 5