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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;

#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($t:ty) =>
        (rl().parse::<$t>().unwrap());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_end().to_owned()
}

const M: usize = 998244353;
fn main() {
    let (n, m, k) = read!(usize, usize, usize);
    let b = {
        let mut tmp = vec![0; k+1];
        tmp[0] = pow_mod(m-1, n-1-k, M);
        for i in 1..k+1 {
            tmp[i] = (tmp[i-1] * (m-1)) % M;
        }
        tmp
    };

    let c = {
        let mut tmp = vec![1; k+1];
        for i in 1..k+1 {
            tmp[i] = (((tmp[i-1] * (n-i)) % M) * pow_mod(i, M-2, M)) % M;
        }
        tmp
    };

    let ans_per_m = b.iter().rev().zip(c.iter()).fold(0usize, |acc, (eb, ec)| (acc + eb * ec) % M);
    println!("{}", (ans_per_m * m) % M);    
}

/// a.pow(b) mod m
fn pow_mod(a: usize, mut b: usize, m: usize) -> usize {
    let mut t = a;
    let mut ans = 1;
    while b != 0 {
        if (b & 1) != 0 {
            ans = (ans * t) % m;
        }
        b >>= 1;
        t = (t * t) % m;
    }
    ans
}