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)

use proconio::input;

const MOD:i64 = 998244353;

fn powm(mut x:i64,mut k:i64) -> i64{
    let mut res = 1i64;
    while k>0 {
        if k&1==1 {
            res=res*x%MOD;
        }
        k>>=1;
        x=x*x%MOD;
    }
    res
}

fn minv(x:i64) -> i64{
    powm(x,MOD-2)
}

fn main() {
    input! {
        n:usize,
        m:usize,
        k:usize
    };
    let fact = {
        let mut fact = vec![1i64;n+1];
        for i in 0..n {
            fact[i+1] = fact[i]*(i+1) as i64%MOD;
        }
        fact
    };

    let comb=|n,k| {
        fact[n] * minv(fact[k])%MOD*minv(fact[n-k])%MOD
    };
    let mut ans = 0i64;
    for dup in 0..(k+1) {
        let pat = m as i64 * comb(n-1,dup)%MOD * powm((m-1) as i64,(n-1-dup) as i64)%MOD;
        ans+=pat;
        ans%=MOD;
    }
    println!("{}",ans);
   
}