There are $N$ balls numbered $1$ through $N$. Ball $i$ is painted in Color $a_i$.

For a permutation $P = (P_1, P_2, \dots, P_N)$ of $(1, 2, \dots, N)$, let us define $C(P)$ as follows:

-   The number of pairs of adjacent balls with different colors when Balls $P_1, P_2, \dots, P_N$ are lined up in a row in this order.

Let $S_N$ be the set of all permutations of $(1, 2, \dots, N)$. Also, let us define $F(k)$ by:

$\displaystyle F(k) = \left(\sum_{P \in S_N}C(P)^k \right) \bmod 998244353$.

Enumerate $F(1), F(2), \dots, F(M)$.

Input is given from Standard Input in the following format:

```
$N$ $M$
$a_1$ $a_2$ $\dots$ $a_N$
```

Print the answers in the following format:

```
$F(1)$ $F(2)$ $\dots$ $F(M)$
```

-   $2 \leq N \leq 2.5 \times 10^5$
-   $1 \leq M \leq 2.5 \times 10^5$
-   $1 \leq a_i \leq N$
-   All values in input are integers.

8 12 20 36

Here is the list of all possible pairs of (P,C(P)).

• If P=(1,2,3), then C(P)=1.
• If P=(1,3,2), then C(P)=2.
• If P=(2,1,3), then C(P)=1.
• If P=(2,3,1), then C(P)=2.
• If P=(3,1,2), then C(P)=1.
• If P=(3,2,1), then C(P)=1.

We may obtain the answers by assigning these values into F(k). For instance, $F(1)=1^1+2^1+1^1+2^1+1^1+1^1=8$.