CF1278F.Cards

Consider the following experiment. You have a deck of $m$ cards, and exactly one card is a joker. $n$ times, you do the following: shuffle the deck, take the top card of the deck, look at it and return it into the deck.

Let $x$ be the number of times you have taken the joker out of the deck during this experiment. Assuming that every time you shuffle the deck, all $m!$ possible permutations of cards are equiprobable, what is the expected value of $x^k$? Print the answer modulo $998244353$.

考虑以下实验：你有一副 $m$ 张牌的牌堆，其中恰好有一张是王牌（joker）。重复进行 $n$ 次如下操作：洗牌，取出牌堆最上方的一张牌，查看其花色后将其放回牌堆。

设 $x$ 为该实验中取出王牌的次数。假设每次洗牌时，所有 $m!$ 种可能的牌序排列都是等概率的，求 $x^k$ 的期望值。请输出答案对 $998244353$ 取模的结果。

The only line contains three integers $n$, $m$ and $k$ ($1 \le n, m \lt 998244353$, $1 \le k \le 5000$).

唯一的一行包含三个整数 $n$、$m$ 和 $k$（$1 \le n, m \lt 998244353$，$1 \le k \le 5000$）。

Print one integer — the expected value of $x^k$, taken modulo $998244353$ (the answer can always be represented as an irreducible fraction $\frac{a}{b}$, where $b \mod 998244353 \ne 0$; you have to print $a \cdot b^{-1} \mod 998244353$).

输出一个整数——$x^k$ 的期望值对 $998244353$ 取模的结果（答案总可表示为既约分数 $\frac{a}{b}$，其中 $b \bmod 998244353 \ne 0$；你需要输出 $a \cdot b^{-1} \bmod 998244353$）。