There are N blocks arranged in a row. Let us paint these blocks.
We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.
Find the number of ways to paint the blocks under the following conditions:
- For each block, use one of the M colors, Color 1 through Color M, to paint it. It is not mandatory to use all the colors.
- There may be at most K pairs of adjacent blocks that are painted in the same color.
Since the count may be enormous, print it modulo 998244353.

-----Constraints-----
- All values in input are integers.
- $1 \leq N, M \leq 2 \times 10^5$
- $0 \leq K \leq N - 1$

-----Input-----
Input is given from Standard Input in the following format:
N M K

-----Output-----
Print the answer.

-----Sample Input-----
3 2 1

-----Sample Output-----
6

The following ways to paint the blocks satisfy the conditions: 112, 121, 122, 211, 212, and 221. Here, digits represent the colors of the blocks.

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