simple counting problem

Given $m, b, c, n$, please calculate the number of sequence $x_1, x_2, x_3, \dots, x_m$ which satisfies :
$0 \leq x_i\leq b ^ i - c, x_i \in \mathbb{Z}$
$\sum_{i = 1}^{m}{x_i} < n$.
Output the answer module 998244353.
$1\leq m\leq 50$
$2\leq b \leq 10^9, -b + 2 \leq c \leq b - 1$
$1\leq n< b^{m + 1}$

There are several test cases, please keep reading until EOF.
For each test case, the first line consists of 3 integers $m, b, c$.
The next line consists of a big integer $n$.
There are 10 test cases.

For each test case, output Case #x: y, which means the the test case number and the answer.

2 2 1
3

Case #1: 5

2017 Multi-University Training Contest - Team 3