计数序列 - 문제

#12354. 计数序列

통계

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

给定四个整数 $m, b, c$ 和 $n$，计算满足以下条件的整数序列 $x_1, \dots, x_m$ 的数量：

$0 \le x_i \le b^i - c$；
$\sum_{i=1}^{m} x_i < n$。

输出答案对 $998\,244\,353$ 取模的结果。

输入格式

第一行包含三个整数 $m, b$ 和 $c$ ($1 \le m \le 50, 2 \le b \le 10^9, -b + 2 \le c \le b - 1$)。第二行包含一个大整数 $n$ ($1 \le n \le b^{m+1}$)。

输出格式

输出一个整数：满足条件的序列数量对 $998\,244\,353$ 取模的结果。

样例

输入格式 1

2 3 1
5

输出格式 1

Editorials

ID	Type	Status	Title	Posted By	Last Updated	Actions
#1818	Editorial	Open	New Editorial for Problem #12354	zrczrczrczrc	2026-05-27 17:24:49	View

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