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

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define all(v) v.begin(), v.end()
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define Rep(n) for (ll _ = 0; _ < (ll)(n); _++)
#define fs first
#define sc second
#define _GLIBCXX_DEBUG

template <class S> S sum(vector<S> &a) { return accumulate(all(a), S()); }
template <class S> S max(vector<S> &a) { return *max_element(all(a)); }
template <class S> S min(vector<S> &a) { return *min_element(all(a)); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }

template <class S> void print(vector<S> &v) {
  for (ll i = 0; i < (ll)v.size(); i++) {
    cerr << v[i] << ' ';
  }
  cerr << endl;
}
template <class S> void print(vector<vector<S>> &v) {
  for (ll i = 0; i < (ll)v.size(); i++) {
    for (ll j = 0; j < (ll)v[i].size(); j++) {
      cerr << v[i][j] << ' ';
    }
    cerr << endl;
  }
}

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; }
};
mint comb(int n, int r) {
  mint si(1);
  mint bo(1);
  for (int i = 0; i < r; i++) {
    bo *= (i + 1);
    si *= (n - i);
  }
  return si / bo;
}
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

int main() {
  int n, m, k;
  cin >> n >> m >> k;
  mint ans;
  mint color(m - 1);
  color = color.pow(n - k - 1) * m;
  mint kumi = comb(n - 1, k);
  for (int p = k; p >= 0; p--) {
    ans += kumi * color;
    color *= (m - 1);
    kumi = kumi * p / (n - p);
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define all(v) v.begin(), v.end()
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define Rep(n) for (ll _ = 0; _ < (ll)(n); _++)
#define fs first
#define sc second
#define _GLIBCXX_DEBUG

template <class S> S sum(vector<S> &a) { return accumulate(all(a), S()); }
template <class S> S max(vector<S> &a) { return *max_element(all(a)); }
template <class S> S min(vector<S> &a) { return *min_element(all(a)); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }

template <class S> void print(vector<S> &v) {
  for (ll i = 0; i < (ll)v.size(); i++) {
    cerr << v[i] << ' ';
  }
  cerr << endl;
}
template <class S> void print(vector<vector<S>> &v) {
  for (ll i = 0; i < (ll)v.size(); i++) {
    for (ll j = 0; j < (ll)v[i].size(); j++) {
      cerr << v[i][j] << ' ';
    }
    cerr << endl;
  }
}

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; }
};
mint comb(int n, int r) {
  mint si(1);
  mint bo(1);
  for (int i = 0; i < r; i++) {
    bo *= (i + 1);
    si *= (n - i);
  }
  return si / bo;
}
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

int main() {
  int n, m, k;
  cin >> n >> m >> k;
  mint ans;
  mint color(m - 1);
  color = color.pow(n - k - 1) * m;
  for (int p = k; p >= 0; p--) {
    ans += comb(n - 1, p) * color;
    color *= (m - 1);
  }
  cout << ans << endl;
}