Score : $500$ points

Problem Statement

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.

3 2 1

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.

100 100 0

73074801

60522 114575 7559

479519525