You are given a formal power series $f(x) = \sum_{i=0}^{N-1} a_i x^i \in \mathbb{Q}[[x]]$ with $a_0 = 0$.
Only $K$ coefficients of $f$ are non-zero, and only such coefficients $a_{i_k}$ are given from input. 

Calculate the first $N$ terms of $\exp(f(x)) = \sum_{i=0}^{\infty} b_i x^i$.
In other words, find $g(x) = \sum_{i=0}^{N-1} b_i x^i \in \mathbb{Q}[[x]]$ such that

$g(x) \equiv \sum_{k=0}^{N-1} \frac{f(x)^k}{k!} \pmod{x^N}.$

Print the coefficients modulo $998244353$.

$N$ $K$
$i_0$ $a_{i_0}$
$\vdots$
$i_{K-1}$ $a_{i_{K-1}}$

$b_0$ $b_1$ $\cdots$ $b_{N - 1}$

- $1 \leq N \leq 10^6$
- $0 \leq K \leq 10$
- $0 < i_0 < \cdots < i_{K-1} \leq N - 1$
- $1 \leq a_{i_k} < 998244353$