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 × 223 + 1, a prime number).
输入描述:
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, ..., cn. (1 ≤ ci ≤ 105).
输出描述:
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).
示例1
输入
2 3<br />1 2<br />3 10<br />9 4 3<br />5 10<br />13 10 6 4 15<br />
输出
1<br />3<br />9<br />0<br />0<br />1<br />1<br />0<br />2<br />4<br />2<br />6<br />15<br />0<br />0<br />0<br />1<br />0<br />1<br />0<br />2<br />0<br />5<br />
备注:
In the first example, there are 9 good vertex-weighted rooted binary trees whose weight exactly equal to 3:
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