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

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;

// 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; }

mint c(ll n, ll k) {
  mint md = 1;
  mint me = 1;
  rep(i, k) {
    md *= (n - i);
    me *= (k - i);
  }
  md *= me.inv();
  return md;
}

int main() {
  int n, m, k;
  cin >> n >> m >> k;
  mint ans(0);
  mint mb(m - 1);
  mint mbpow = mb.pow(n - k - 1);
  mint ccc = c(n - 1, k);
  rep(i, k + 1) {
    mint ma(m);
    ma *= mbpow;
    ma *= ccc;
    ans += ma;
    mbpow *= mb;
    ccc *= k - i;
    ccc /= (n - k + i);
  }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;

// 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; }

mint c(ll n, ll k) {
  mint md = 1;
  mint me = 1;
  rep(i, k) {
    md *= (n - i);
    me *= (k - i);
  }
  md *= me.inv();
  return md;
}

int main() {
  int n, m, k;
  cin >> n >> m >> k;
  mint ans(0);
  mint mb(m - 1);
  mint mbpow = mb.pow(n - k - 1);
  mint ccc = c(n - 1, k);
  rep(i, k + 1) {
    mint ma(m);
    ma *= mbpow;
    ma *= c(n - 1, k - i);
    ans += ma;
    mbpow *= mb;
    ccc *= k - i;
    ccc /= (n - k + i);
  }
  cout << ans << endl;
  return 0;
}