The Child and Binary Tree

题目描述

Our child likes computer science very much, especially he likes binary trees. Consider the sequence of $n$ distinct positive integers: $c_{1},c_{2},...,c_{n}$ . The child calls a vertex-weighted rooted binary tree good if and only if for every vertex $v$ , the weight of $v$ is in the set ${c_{1},c_{2},...,c_{n}}$ . Also our child thinks that the weight of a vertex-weighted tree is the sum of all vertices' weights. Given an integer $m$ , can you for all $s$ $(1<=s<=m)$ calculate the number of good vertex-weighted rooted binary trees with weight $s$ ? Please, check the samples for better understanding what trees are considered different. We only want to know the answer modulo $998244353$ ( $7×17×2^{23}+1$ , a prime number).

输入输出格式

输入格式

The first line contains two integers $n,m$ $(1<=n<=10^{5}; 1<=m<=10^{5})$ . The second line contains $n$ space-separated pairwise distinct integers $c_{1},c_{2},...,c_{n}$ . $(1<=c_{i}<=10^{5})$ .

输出格式

Print $m$ lines, each line containing a single integer. The $i$ -th line must contain the number of good vertex-weighted rooted binary trees whose weight exactly equal to $i$ . Print the answers modulo $998244353$ ( $7×17×2^{23}+1$ , a prime number).

输入输出样例

输入样例 #1

2 3
1 2


输出样例 #1

1
3
9


输入样例 #2

3 10
9 4 3


输出样例 #2

0
0
1
1
0
2
4
2
6
15


输入样例 #3

5 10
13 10 6 4 15


输出样例 #3

0
0
0
1
0
1
0
2
0
5


说明

In the first example, there are $9$ good vertex-weighted rooted binary trees whose weight exactly equal to $3$ : ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF438E/eac2c310aa15e844747811a6717476e6a022e10e.png)