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: Accepted)

#include <bits/stdc++.h>

#define st first
#define nd second
#define ll long long
#define ld long double
#define pb push_back
#define emp emplace_back
#define pii pair<int, int>
#define usg unsigned
#define sg signed
#define mp make_pair

using namespace std;

void setIO(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
}

const ld PI = 4*atan((ld)1);
const int INF = 1e9+7;
const int MOD = 998244353;
const int mxN = 2e5+7;

ll f[mxN+7];

ll expo(ll x, ll y){
	ll res=1;
	while(y){
		if(y&1) res=(res*x)%MOD;
		x = (x*x)%MOD;
		y>>=1;
	}
	return res%MOD;
}

void fact(){
	f[0]=1;
	for(ll i=1;i<=mxN;i++)
		f[i]=(f[i-1]*i)%MOD;
}

ll com(ll n, ll r){
	return (((f[n]*expo(f[n-r],MOD-2))%MOD)*expo(f[r], MOD-2))%MOD;
}

int main(){
	setIO();
	fact();
	ll n, m, k,ans=0;
	cin>>n>>m>>k;
	for(ll i=0;i<=k;i++){
		ans=(ans+(com(n-1,i)*expo(m-1,n-1-i))%MOD)%MOD;
	}
	cout<<(ans*m)%MOD<<endl;
}