Problem:
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.

Sample Input 1

3 2 1

Sample Output 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.

Sample Input 2

100 100 0

Sample Output 2

73074801

Sample Input 3

60522 114575 7559

Sample Output 3

479519525

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

jo = 998244353;

memo = {}
function calc(n,m,k){
	key = String(n)+"/"+String(k)
	if (!(key in memo)){
		if (k < 0){
			ans = 0
		}else if (n == 1){
			ans = m%jo
		}else{
			raw_ans = calc(n-1,m,k-1) + (m-1)*calc(n-1,m,k)
			ans = raw_ans % jo
		}
		memo[key] = ans
	}
	return memo[key]
}

s = require('fs').readFileSync('/dev/stdin', 'utf8');
[s0,s1,s2] = s.split(" ")
n0 = Number(s0)
m0 = Number(s1)
k0 = Number(s2)
ans = calc(n0,m0,k0)
console.log(ans)