9000: [yosupo] Enumerative Combinatorics - $\#_p$ Subset Sum
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Description
Given $N$ positive integers $s_0,s_1,\ldots,s_{N-1}$ and a positive integer $T$.
For each $t=1,2,...,T$, count the number of subset $I \subseteq \\{0,1,...,N-1\\}$ s.t. $\sum_{i \in I} s_i=t$ and print it $\bmod {998244353}$ (we denote it as $p_t$).
For each $t=1,2,...,T$, count the number of subset $I \subseteq \\{0,1,...,N-1\\}$ s.t. $\sum_{i \in I} s_i=t$ and print it $\bmod {998244353}$ (we denote it as $p_t$).
Input
$N$ $T$
$s_0$ $s_1$ ... $s_{N-1}$
$s_0$ $s_1$ ... $s_{N-1}$
Output
$p_1$ $p_2$ ... $p_T$
Constraints
$1 \leq N \leq 10^6$
$1 \leq T \leq 5 \times 10^5$
$1 \leq s_i \leq T$
$1 \leq T \leq 5 \times 10^5$
$1 \leq s_i \leq T$
Sample 1 Input
5 3
1 1 2 2 3
Sample 1 Output
2 3 5