Problem Statement

You are given $a sequence (A_1, A_2, \ldots , A_N)$.
Let us define $a sequence (F_0, F_1, \ldots , F_N)$ by the following formulae.

• F_0 = 1
• $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j (1 \leq n \leq N)$

Find $F_1, \ldots , F_N modulo 998244353$.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$

Output

Print $F_1, \ldots , F_N modulo 998244353$ in this order, with spaces in between.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i < 998244353$
• All input values are integers.

Sample Input 1

5
1 2 3 4 5

Sample Output 1

1 6 48 496 6240

F_1 = A_1F_0F_0 = 1.
F_2 = A_2(F_0F_0+F_0F_1+F_1F_0) = 6.
Similarly, we find F_3 = 48, F_4 = 496, F_5 = 6240.

Sample Input 2

3
12345 678901 2345678

Sample Output 2

12345 790834943 85679169

见题面 Input 部分

见题面 Output 部分