Problem p02685 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 998244353;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
  mint p(int n, int k) { return fact[n] * ifact[n - k]; }
} c(200005);

int main() {
  int N, M, K;
  cin >> N >> M >> K;
  // 前処理
  mint nRet = 0;
  mint tmp = 1;
  for (int n = 0; n < N - 1 - K; ++n) {
    tmp *= M - 1;
  }
  for (int k = K; k >= 0; --k) {
    mint ntemp = (mint)M * c(N - 1, k);
    ntemp *= tmp;
    nRet += ntemp;
    tmp *= M - 1;
  }
  cout << nRet << endl;
}

Error: TLE

Fixed submission:

#include "bits/stdc++.h"

using namespace std;

const int MAX = 510000;
const int MOD = 998244353;

long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

// 二項係数計算
long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

constexpr int mod = 998244353;
class mint {
public:
  long long x;
  constexpr mint(long long x = 0) : x((x % mod + mod) % mod) {}
  constexpr mint operator-() const { return mint(-x); }
  constexpr mint &operator+=(const mint &a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  constexpr mint &operator-=(const mint &a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  constexpr mint &operator*=(const mint &a) {
    (x *= a.x) %= mod;
    return *this;
  }
  constexpr mint operator+(const mint &a) const {
    mint res(*this);
    return res += a;
  }
  constexpr mint operator-(const mint &a) const {
    mint res(*this);
    return res -= a;
  }
  constexpr mint operator*(const mint &a) const {
    mint res(*this);
    return res *= a;
  }
  constexpr mint pow(long long t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  constexpr mint inv() const { return pow(mod - 2); }
  constexpr mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
  constexpr mint operator/(const mint &a) const {
    mint res(*this);
    return res /= a;
  }
};
ostream &operator<<(ostream &os, const mint &m) {
  os << m.x;
  return os;
}

int main() {
  int N, M, K;
  cin >> N >> M >> K;
  // 前処理
  COMinit();
  mint nRet = 0;
  for (int k = 0; k <= K; ++k) {
    mint ntemp = M * COM(N - 1, k);
    for (int l = 0; l < (N - 1 - k); ++l) {
      ntemp *= (M - 1);
    }
    nRet += ntemp;
  }
  cout << nRet << endl;
}