Agent $04$ is a very dangerous person. He has an army of $n$ people, and this army guards the divine cattle.

Each person in the army has a rank, and all ranks are distinct. As the Year of the Gengzi passes and the Year of the Xinchou arrives, the person who was originally at rank $i$ will have a new rank of $p_i$, where $p$ is a permutation.

For the person who was originally at rank $i$, if $p_i > p_{i+1}$, it means their new rank is not higher than the person who was originally ranked lower than them, which makes them unhappy. Specifically, the person who was originally at the lowest rank cannot be unhappy.

You have a subordinate who infiltrated Agent $04$'s army early on, and his rank in the past year was $k$. He has found out that the total number of unhappy people (including himself) is $m$.

You want to know, for each $l$ where $1 \le l \le n$, how many possible permutations exist such that your subordinate's new rank is $l$, to facilitate your future rescue mission. The number of ways should be taken modulo $998244353$.

Input

A single line containing three integers $n, m, k$.

Output

A single line containing $n$ integers, representing the number of possible permutations for each $l$ from $1$ to $n$, modulo $998244353$.

Examples

Input 1

4 2 1

Output 1

1 2 4 4

Input 2

5 0 2

Output 2

0 1 0 0 0

Input 3

11 2 4

Output 3

14880 14160 12816 11640 11496 12480 13896 15093 15696 15600 14880

Input 4

See ex_army4.in and ex_army4.ans in the download files. This sample satisfies the constraints of Subtask $3$.

Constraints

For $100\%$ of the data, $1 \le n \le 5 \times 10^5$, $0 \le m \le n-1$, $1 \le k \le n$.