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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

//F
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int l = 0,r = 0;
int main(){
	int n;
	cin >> n;
	int ok1 = 0,ok2 = 0,well = 1;
	for(int i = 1;i <= n;i++){
		string s;
		cin >> s;
		int tl = 0,tr = 0;
		for(char x:s){
			if(x == '(')tl++;
			else if(x == ')'){
				if(tl > 0)tl--;
				else tr++;
			}
		}
		if((tl and !tr))ok1 = 1;
		if(!tl and tr)ok2 = 1;
		if(tl or tr)well = 0;
		l += tl,r += tr;
//		cout << tl << " " << tr << endl;
	}
	if(well or (ok1 and ok2 and l == r))cout << "Yes";
	else cout << "No";
	return 0;
}