CF1081C.Colorful Bricks

On his free time, Chouti likes doing some housework. He has got one new task, paint some bricks in the yard.

There are $n$ bricks lined in a row on the ground. Chouti has got $m$ paint buckets of different colors at hand, so he painted each brick in one of those $m$ colors.

Having finished painting all bricks, Chouti was satisfied. He stood back and decided to find something fun with these bricks. After some counting, he found there are $k$ bricks with a color different from the color of the brick on its left (the first brick is not counted, for sure).

So as usual, he needs your help in counting how many ways could he paint the bricks. Two ways of painting bricks are different if there is at least one brick painted in different colors in these two ways. Because the answer might be quite big, you only need to output the number of ways modulo $998\,244\,353$.

空闲时，Chouti 喜欢做些家务。他刚接到一项新任务：粉刷院子里的一些砖块。

地面上有 $n$ 块砖排成一排。Chouti 手头有 $m$ 桶不同颜色的油漆，因此他将每块砖涂成了这 $m$ 种颜色中的一种。

完成所有砖块的粉刷后，Chouti 感到非常满意。他向后退了几步，决定用这些砖块找点乐子。经过一番计数，他发现恰好有 $k$ 块砖的颜色与其左侧相邻砖块的颜色不同（第一块砖显然不计入统计）。

因此，照例，他需要你帮忙计算：有多少种不同的粉刷方案？两种粉刷方案被视为不同，当且仅当至少有一块砖在两种方案中被涂上了不同的颜色。由于答案可能非常大，你只需输出结果对 $998\,244\,353$ 取模后的值。

The first and only line contains three integers $n$, $m$ and $k$ ($1 \leq n,m \leq 2000, 0 \leq k \leq n-1$) — the number of bricks, the number of colors, and the number of bricks, such that its color differs from the color of brick to the left of it.

第一行且唯一一行包含三个整数 $n$、$m$ 和 $k$（$1 \leq n,m \leq 2000$，$0 \leq k \leq n-1$）——分别表示砖块数量、颜色种类数，以及颜色与其左侧砖块颜色不同的砖块数量。

Print one integer — the number of ways to color bricks modulo $998\,244\,353$.

输出一个整数——染色砖块的方案数对 $998\,244\,353$ 取模的结果。

In the first example, since $k=0$, the color of every brick should be the same, so there will be exactly $m=3$ ways to color the bricks.

In the second example, suppose the two colors in the buckets are yellow and lime, the following image shows all $4$ possible colorings.

在第一个例子中，由于 $k=0$，每块砖的颜色都必须相同，因此恰好有 $m=3$ 种给砖块上色的方法。

在第二个例子中，假设桶中的两种颜色为黄色和青柠色，下图展示了全部 $4$ 种可能的上色方案。