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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

const input = require("fs").readFileSync("/dev/stdin", "utf8")

function pow (x ,n) {
    let res = 1n
    while (n > 0) {
        if (n & 1n) res = res * x % mod
        x = x * x % mod
        n >>= 1n
    }
    return res
}

function fact (n) {
    let res = 1n
    for (n; n > 1; n--) {
        res = res * n
    }
    return res
}

function fact2 (n, m) {
    let res = 1n
    for (n; n <= m; n++) {
        res = res * n
    }
    return res
}

const mod = 998244353n

;(input => {
    const lines = input.split('\n')
    let [N, M, K] = lines[0].split(' ').map(Number)
    N = BigInt(N)
    M = BigInt(M)
    K = BigInt(K)

    let ans = 0n
    for (let k = 0n; k <= K; k++) {
        let left = fact2(N - k, N - 1n) / fact(k)
        ans += left * pow((M - 1n), (N - (k + 1n))) * M % mod
    }

    console.log((ans % mod).toString())
 
})(input)