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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        n: usize,
        m: u64,
        k: usize,
    }
    let mut c=vec![0;n];
    c[0]=1;
    for i in 1..n {
        let mut x=i as u64;
        let mut y=1;
        let mut j=MOD-2;
        while j>0 {
            if j&1==1 {
                y=y*x%MOD;
            }
            x=x*x%MOD;
            j>>=1;
        }
        c[i]=c[i-1]*(n-i)as u64%MOD*y%MOD;
    }
    let mut p=vec![0;n];
    p[0]=m;
    for i in 1..n {
        p[i]=p[i-1]*(m-1)%MOD;
    }
    let mut t=0;
    for i in 0..=k {
        t = (t+c[i]*p[n-i-1]%MOD)%MOD;
    }
    println!("{}",t);
}
const MOD: u64=998244353;