Colorful Blocks

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.

Examples

Input

3 2 1

Output

6

Input

100 100 0

Output

73074801

Input

60522 114575 7559

Output

479519525

inputFormat

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

outputFormat

Output

Print the answer.

Examples

Input

3 2 1

Output

6

Input

100 100 0

Output

73074801

Input

60522 114575 7559

Output

479519525

样例

100 100 0

73074801