Our child likes computer science very much, especially he likes binary trees.

Consider the sequence of n distinct positive integers: c₁, c₂, ..., 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 {c₁, c₂, ..., 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 × 2²³ + 1, a prime number).

Input

The first line contains two integers n, m (1 ≤ n ≤ 10⁵; 1 ≤ m ≤ 10⁵). The second line contains n space-separated pairwise distinct integers c₁, c₂, ..., c_n. (1 ≤ c_i ≤ 10⁵).

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 × 2²³ + 1, a prime number).

Note

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

$\text{[math]}$

The Child and Binary Tree

Examples