时间限制:C/C++/Rust/Pascal 3秒,其他语言6秒
空间限制:C/C++/Rust/Pascal 1024 M,其他语言2048 M
Special Judge, 64bit IO Format: %lld

题目描述

Find the number of labeled trees that satisfy the following conditions:

1. n vertices.
2. Each vertex has a degree less than or equal to d.
3. There exists a path that includes nodes 1, 2, 3, \cdots, k. Note that this path may also include other nodes.

Output the result modulo 998244353.

输入描述:

The first line contains three positive integers n, d, k.

输出描述:

Output one integer, which is the answer modulo 998244353.
示例1

输入

复制
4 2 2

输出

复制
12
示例2

输入

复制
10 3 4

输出

复制
33957360

备注:

1 \leq d < n \leq 500, 1 \leq k \leq n \leq 500.