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: Accepted)

#include <bits/stdc++.h>
#define all(vec) vec.begin(), vec.end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
template <class T>
using V = vector<T>;
template <class T>
inline void chmin(T &a, const T &b) { a = min(a, b); }
template <class T>
inline void chmax(T &a, const T &b) { a = max(a, b); }
template <class T>
inline bool kbit(const T &x, const int &k) { return ((x >> k) & 1LL); }
inline int popcount(const int &n) { return __builtin_popcount(n); }
inline ll popcountll(const ll &n) { return __builtin_popcountll(n); }
template <class T>
void zip(V<T> &v) {
    sort(all(v));
    v.erase(unique(all(v)), v.end());
}
void dump() {
    cerr << '\n';
}
template <class Head, class... Tail>
void dump(Head &&head, Tail &&... tail) {
    cerr << head << (sizeof...(Tail) == 0 ? " " : " ");
    dump(std::move(tail)...);
}
template <class T>
void print(const vector<T> &v) {
    for (int i = 0; i < v.size(); i++) cout << v[i] << (i + 1 == v.size() ? '\n' : ' ');
}
template <class T>
void read(vector<T> &v) {
    for (int i = 0; i < v.size(); i++) cin >> v[i];
}
constexpr char sp = ' ';
constexpr char newl = '\n';
constexpr int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
constexpr ll INF = (1LL << 30) - 1LL;
constexpr ll MOD = 998244353LL;
//from http://noshi91.hatenablog.com/entry/2019/03/31/174006
template <std::uint_fast64_t Modulus>
class modint {
    using u64 = std::uint_fast64_t;

  public:
    u64 a;
    constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
    constexpr u64 &value() noexcept { return a; }
    constexpr const u64 &value() const noexcept { return a; }
    constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
    }
    constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
    }
    constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
    }
    constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
    }
    constexpr modint operator^(const u64 rhs) const noexcept {
        return modint(*this) ^= rhs;
    }
    constexpr modint &operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr modint &operator-=(const modint rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr modint &operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr modint &operator/=(modint rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    constexpr modint &operator^=(u64 exp) {
        modint rhs = modint(*this);
        a = 1;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    friend ostream &operator<<(ostream &os, const modint &x) {
        os << x.a;
        return os;
    }
    friend istream &operator>>(istream &is, modint &x) {
        is >> x.a;
        return is;
    }
};
using mint = modint<MOD>;
vector<mint> f, fi;
void comb(int n) {
    f.resize(n + 1);
    fi.resize(n + 1);
    f[0] = 1;
    for (ll i = 1; i <= n; i++) {
        f[i] = f[i - 1] * mint(i);
    }
    fi[n] = mint(1) / f[n];
    for (ll i = n - 1; i >= 0; i--) {
        fi[i] = fi[i + 1] * mint(i + 1LL);
    }
}
mint ncr(ll n, ll r) {
    if (n < r) {
        return mint(0);
    }
    if (r == 0) {
        return mint(1);
    }
    return f[n] * fi[n - r] * fi[r];
}
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll n, m, k;
    cin >> n >> m >> k;
    comb(n + 10);
    mint res = 0;
    for (ll i = n - k; i <= n; i++) {
        mint s = ncr(n - 1, i - 1);
        s *= m;
        s *= (mint(m - 1) ^ (i - 1));
        res += s;
    }
    cout << res << newl;
}