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<stdio.h>
#define MODN 998244353

static inline long modadd(long a,long b){
    return (a+b) % MODN;
}

static inline long modml(long a,long b){
    return (long long)a * b % MODN;
}

static inline long modpow(long n,long ind){
    unsigned long cnt = ind;
    long res = 1;
    while(cnt){
        if(cnt & 1ul)res = modml(res,n);
        n = modml(n,n);
        cnt >>= 1;
    }
    return res;
}

static inline long modinv(long n){
    return modpow(n,MODN - 2);
}

long modfact[200200];

static inline long modnck(long n,long k){
    return modml(modfact[n],modinv(modml(modfact[n-k],modfact[k])));
}

int main(void){
    register int i;
    int n,m,k;
    scanf("%d%d%d",&n,&m,&k);
    modfact[0] = 1;
    for(i = 1;i <= n;i++)modfact[i] = modml(modfact[i-1],i);
    long ans = 0;
    for(i = 0;i <= k;i++)ans = modadd(ans,modml(modml(modpow(m-1,n-i-1),m),modnck(n-1,i)));
    printf("%ld",ans);
}