Problem Statement

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

Constraints

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

Input

Input is given from Standard Input in the following format:

N M
a_1 a_2 \dots a_N

Output

Print the answers in the following format:

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