Description

This backpack can hold a total size of at most $10^5$.

Princess Fu has $n$ types of goods and she is about to set up a stall.

Each type has volume $v_i$, and there are infinitely many pieces available.

Given $m$, for $s \in [1,m]$, please answer the number of ways to fill exactly volume $s$ using these goods.

Input Format

The first line contains two positive integers $n, m$. The second line contains $n$ positive integers, representing the volume of each type of good.

Output Format

Output $m$ lines, where the $i$-th line represents the number of ways when $s = i$, taken modulo $998244353$.

2 4
1 2

1
2
2
3

Hint

Constraints
For 30% of the testdata, $1 \le n, m \le 3000$.
For 60% of the testdata, purely randomly generated.
For 100% of the testdata, $1 \le n, m \le 10^5$, $1 \le v_i \le m$.

Translated by ChatGPT 5