RXD and functions

Problem Description

RXD has a polynomial function $f(x)$, $f(x) = \sum_{i = 0}^{n}{c_ix^i}$ RXD has a transformation of function $Tr(f, a)$, it returns another function $g$, which has a property that $g(x) = f(x - a)$. Given $a_1, a_2, a_3, \dots , a_m$, RXD generates a polynomial function sequence $g_i$, in which $g_0 = f$ and $g_i = Tr(g_{i - 1}, a_i)$ RXD wants you to find $g_m$, in the form of $\sum_{i = 0}^{m}{b_ix^i}$ You need to output $b_i$ module 998244353. $n\leq 10^5$

Input

There are several test cases, please keep reading until EOF. For each test case, the first line consists of 1 integer $n$, which means $\deg F$. The next line consists of $n + 1$ intergers $c_i, 0 \leq c_i < 998244353$, which means the coefficient of the polynomial. The next line contains an integer $m$, which means the length of $a$. The next line contains $m$ integers, the i - th integer is $a_i$. There are 11 test cases. $0<=ai<998244353$ $\sum m\leq 10^5$

Output

For each test case, output an polynomial with degree n, which means the answer.

Sample Input

2

0 0 1

1

1

Sample Output

1 998244351 1

Hint

$(x - 1) ^ 2 = x^2 - 2x + 1$

Source

2017 Multi-University Training Contest - Team 3

https://acm.hdu.edu.cn/showproblem.php?pid=6061