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).

Input

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 $*c*_{1}, *c*_{2}, ..., *c*_{*n*}$. $(1 ≤ *c*_{*i*} ≤ 10^{5})$.

Output

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).

Note

In the first example, there are $9$ good vertex-weighted rooted binary trees whose weight exactly equal to $3$: