Problem Statement

You are given positive integers $N, P, Q$.

Here, $P, Q$ are coprime.

For each $n = 1, 2, \dots, N$, answer the following question.

Find the number, modulo $998244353$, of pairs $(A, B)$ of non-negative integer sequences $A = (A_{1}, A_{2}, \dots, A_{n}), B = (B_{1}, B_{2}, \dots, B_{n})$ of length $n$ that satisfy all of the following conditions.

• $\sum A = P$
• $\sum B = Q$
• For every integer $m$ between $1$ and $n$, inclusive, the following holds.
  • $\displaystyle Q\sum_{i = 1}^{m} A_{i} \geq P\sum_{i = 1}^{m} B_{i}$

Constraints

• $1\leq N\leq 5\times 10^{5}$
• $1\leq P\leq 5\times 10^{5}$
• $1\leq Q\leq 5\times 10^{5}$
• $\mathrm{gcd}(P, Q) = 1$
• All input values are integers.

Input

$N$ $P$ $Q$

Output

Print $N$ lines.

On the $i$-th line, print the answer for $n = i$.

Sample

3 1 1

1
3
6

5 2 3

1
7
27
77
182

16 79 24

1
1001
352001
65111501
602454930
711287574
473879682
9649799
360574128
569945347
993487430
346927517
744590286
964120490
323267590
17560896