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: Runtime Error)


long powmod(long a,long b,long m){
    if(b==1){return a;}
    long c;
    c = powmod((a*a)%m,b/2,m);
    if(b%2){
        c=(c*a)%m;
    }
    return c;
}
int main(void){
  long n,m,k;
  long i;
  scanf("%ld %ld %ld", &n, &m, &k);
  long mod = 998244353;
  long sum = m*powmod(m-1,n-1,mod);
  long c=1;
  for(i=1;i<=k;i++){
    c = (c *(((n-i)*powmod(i,mod-2,mod))%mod))%mod;
    sum = (sum + ((m*c)%mod)*powmod(m-1,n-1-i,mod))%mod;
  }
  printf("%ld",sum);
}