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)

#pragma region Macros
#include <bits/stdc++.h>
#define SORT(x) sort((x).begin(), (x).end())
#define RSORT(x) sort((x).rbegin(), (x).rend())
#define ALL(x) (x).begin(), (x).end()
#define REV(x) reverse(ALL(x))
#define rep(i, n) for (ll i = 0; i < n; i++)
#define reps(i, m, n) for (ll i = m; i < n; i++)
#define repr(i, m, n) for (ll i = m; i >= n; i--)
#define SP << " " <<
#define INF2 1000000000000000037
#define INF  1000000007
#define lwb(x,n) distance(x.begin(),lower_bound(ALL(x),(n)))
#define upb(x,n) distance(x.begin(),upper_bound(ALL(x),(n)))
#define fora(i, ...) if(ll i = -1) for(__VA_ARGS__) if(i++, true)
#ifdef _MY_DEBUG
#define isdebug true
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,x,...) x
#define debug_1(x1) cout<<#x1<<": "<<x1<<endl
#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl
#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl
#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl
#define de(...) CHOOSE((__VA_ARGS__,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)
#else
#define isdebug false
#define de(...)
#endif
using namespace std;
using ll = long long;
using ld = long double;
const ld PI = 3.14159265358979323846;
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
template<class T = ll> using v = vector<T>;
template<class T = ll> using vv = vector<vector<T>>;
template<class T = ll> using vvv = vector<vector<vector<T>>>;
template<class T> bool maxi(T &a, const T &b){ if(a<b){a=b;return 1;}return 0;}
template<class T> bool mini(T &a, const T &b){ if(b<a){a=b;return 1;}return 0;}
template<class T> ll sumer(const T& a){ return accumulate(ALL(a),0LL); }
template<class T> void UNIQUE(vector<T> &a){ SORT(a);a.erase(unique(ALL(a)),a.end());}
template<class T, class U> ostream &operator<<(ostream &os, const pair<T,U> &pe) { os << pe.first << " " << pe.second; return os;}
template<class T> ostream &operator<<(ostream &os, const v<T> &ve) { rep(i,ve.size()) os<< (i?" ":"")<<ve[i]; return os;}
ll topbit(ll a) { return a==0?-1:63-__builtin_clzll(a);}
ll botbit(ll a) { return a==0?64:__builtin_ctzll(a);}
ll popcount(ll a) { return __builtin_popcountll(a);}
#define dame {cout<< retword <<"\n"; return;}
#pragma endregion
//--MODIFS---------------------------------
#pragma region Modifs
#define retword "-1"
#define MOD  998244353
const ld EPS = 1e-9;
using P  = pair<ll,ll>;
using TP  = tuple<ll,ll,ll>;
#pragma endregion
//--GLOBAL---------------------------------
const ll MAX = 202020;
ll fac[MAX], finv[MAX], inv[MAX];
void cinit() { // O(nlogn)
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    reps(i, 2, MAX){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
ll c(int n, int k){ // 二項係数計算
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

template< int mod >
struct ModInt {
    ll x;

    ModInt() : x(0) {}
    ModInt(ll y) : x(y >= 0 ? ( y<mod ? y : y%mod ) : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inv();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    bool operator<(const ModInt &p) const {return x < p.x; }

    ModInt operator+(const ll &q) const {return ModInt(*this) += (ModInt)q; }
    ModInt operator-(const ll &q) const {return ModInt(*this) -= (ModInt)q; }
    ModInt operator*(const ll &q) const {return ModInt(*this) *= (ModInt)q; }
    ModInt operator/(const ll &q) const {return ModInt(*this) /= (ModInt)q; }
    bool operator==(const ll &q) const {return x == q; }
    bool operator!=(const ll &q) const {return x != q; }

    ModInt operator++(){ if(++x == mod) x = 0; return *this; }
    ModInt operator--(){ x = (x == 0 ? mod-1 : x-1); return *this; }
    ModInt operator++(int){ const ModInt res(*this); ++*this; return res; }
    ModInt operator--(int){ const ModInt res(*this); --*this; return res; }

    ModInt inv() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(ll n, bool inv=false) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
        if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        if(inv) ret=ret.inv();
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is, ModInt &a) {
        ll t;
        is >> t;
        a = ModInt< mod >(t);
        return (is);
    }
};
using mint = ModInt< MOD >;
mint mpow(ll x, ll n, bool inv=false) {
    mint ret(1), mul(x);
    while(n > 0) {
    if(n & 1) ret *= mul;
        mul *= mul;
        n >>= 1;
    }
    if(inv) ret=ret.inv();
    return ret;
}
vector<mint> powpool;
void makepow(ll num, ll pool, bool inv=false){
    mint now=1;
    if(inv) makepow((now/num).x ,pool);
    rep(i,pool+1){
        powpool.emplace_back(now);
        now*=num;
    }
}
mint poolpow(ll n){
    if(n>=powpool.size()) return powpool[1].pow(n);
    return powpool[n];
}
// .inv() .pow(n,bool) mpow(x,n,bool)  makepow(x,n,bool)->poolpow(n)
//--MAIN-----------------------------------
void Main() {
    ll N,M,K;
    cin>>N>>M>>K;
    mint ans=0;
    cinit();
    rep(k,K+1){
        mint buf=M;
        buf*=c(N-1,k);
        buf*=mpow(M-1,N-1-k);
        ans+=buf;
    }

    cout<< ans<<"\n";
    
}
//--START----------------------------------
int main() {
    cin.tie(nullptr); ios_base::sync_with_stdio(false);
    // if(isdebug) {ifstream in("input.txt"); cin.rdbuf(in.rdbuf());}
    // if(isdebug) {ofstream out("output.txt"); cout.rdbuf(out.rdbuf());}
    cout << fixed << setprecision(15);
    // ll Qkai; cin>>Qkai; rep(QQ,Qkai) Main();
    Main();
}
//-----------------------------------------