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

#include "bits/stdc++.h"

using namespace std;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef vector<PII> VPII;
typedef long long LL;
typedef priority_queue<int> PQ_DESC;
typedef priority_queue<int, vector<int>, greater<int>> PQ_ASC;
typedef priority_queue<PII> PQ_DESC_PII;
typedef priority_queue<PII, vector<PII>, greater<PII>> PQ_ASC_PII;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<VVLL> VVVLL;

#define SORT_ASC(c) sort((c).begin(), (c).end())
#define SORT_DESC(c)                                                           \\
  sort((c).begin(), (c).end(), greater<typeof((c).begin())>())

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define FORL(i, a, b) for (LL i = (a); i < (b); ++i)
#define REPL(i, n) FORL(i, 0, n)
#define SIZE(a) int((a).size())
#define ALL(a) (a).begin(), (a).end()

const double EPS = 1e-10;
const double PI = acos(-1.0);

// debug func
template <typename T> void vprint(vector<T> v) {
  for (auto x : v) {
    cerr << x << " ";
  }
  cerr << endl;
}

template <typename T> void vvprint(vector<vector<T>> vv) {
  REP(i, SIZE(vv)) {
    REP(j, SIZE(vv[i])) { cerr << vv[i][j] << " "; }
    cerr << endl;
  }
}

template <typename Iterator>
inline bool next_combination(const Iterator first, Iterator k,
                             const Iterator last) {
  /* Credits: Thomas Draper */
  if ((first == last) || (first == k) || (last == k))
    return false;
  Iterator itr1 = first;
  Iterator itr2 = last;
  ++itr1;
  if (last == itr1)
    return false;
  itr1 = last;
  --itr1;
  itr1 = k;
  --itr2;
  while (first != itr1) {
    if (*--itr1 < *itr2) {
      Iterator j = k;
      while (!(*itr1 < *j))
        ++j;
      iter_swap(itr1, j);
      ++itr1;
      ++j;
      itr2 = k;
      rotate(itr1, j, last);
      while (last != j) {
        ++j;
        ++itr2;
      }
      rotate(k, itr2, last);
      return true;
    }
  }
  rotate(first, k, last);
  return false;
}

inline double get_time_sec(void) {
  return static_cast<double>(chrono::duration_cast<chrono::nanoseconds>(
                                 chrono::steady_clock::now().time_since_epoch())
                                 .count()) /
         1000000000;
}

template <typename T> T gcd(T a, T b) {
  if (a > b)
    swap(a, b);
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}

template <typename T> T lcm(T a, T b) { return (a / gcd(a, b)) * b; }

template <typename T> map<T, T> prime_list(T n) {
  map<T, T> ret;
  for (T i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret[i] = 0;
      while (n % i == 0) {
        n /= i;
        ret[i]++;
      }
    }
  }
  if (n != 1)
    ret[n]++;
  return ret;
}

#define MOD 998244353

LL mypow(LL a, LL n) {
  if (n == 0)
    return 1;
  if (n == 1)
    return a % MOD;
  if (n % 2 == 1)
    return (a * mypow(a, n - 1)) % MOD;
  LL t = mypow(a, n / 2);
  return (t * t) % MOD;
}

LL mycomb(LL n, LL k) {
  if (n == 0 || n == k)
    return 1;
  LL x = 1, y = 1;
  REP(i, k) {
    x = x * (n - i) % MOD;
    y = y * (i + 1) % MOD;
  }
  return x * mypow(y, MOD - 2) % MOD;
}

#define INF 1e8

int main(void) {
  int n, m, k;
  cin >> n >> m >> k;
  VLL dp(n, m);
  FOR(i, 1, n) dp[i] = (dp[i - 1] * (m - 1)) % MOD;
  reverse(ALL(dp));

  VLL comb(n, 1);
  FOR(i, 1, n) {
    comb[i] = (comb[i - 1] * (n - i)) % MOD * mypow(i, MOD - 2);
    comb[i] %= MOD;
  }
  // vprint(comb);

  REP(i, k + 1) {
    dp[i] *= comb[i];
    dp[i] %= MOD;
  }
  // vprint(dp);
  LL ans = 0;
  REP(i, k + 1) {
    ans += dp[i];
    ans %= MOD;
  }
  cout << ans << endl;
}

Error: TLE

Fixed submission:

#include "bits/stdc++.h"

using namespace std;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef vector<PII> VPII;
typedef long long LL;
typedef priority_queue<int> PQ_DESC;
typedef priority_queue<int, vector<int>, greater<int>> PQ_ASC;
typedef priority_queue<PII> PQ_DESC_PII;
typedef priority_queue<PII, vector<PII>, greater<PII>> PQ_ASC_PII;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<VVLL> VVVLL;

#define SORT_ASC(c) sort((c).begin(), (c).end())
#define SORT_DESC(c)                                                           \\
  sort((c).begin(), (c).end(), greater<typeof((c).begin())>())

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define FORL(i, a, b) for (LL i = (a); i < (b); ++i)
#define REPL(i, n) FORL(i, 0, n)
#define SIZE(a) int((a).size())
#define ALL(a) (a).begin(), (a).end()

const double EPS = 1e-10;
const double PI = acos(-1.0);

// debug func
template <typename T> void vprint(vector<T> v) {
  for (auto x : v) {
    cerr << x << " ";
  }
  cerr << endl;
}

template <typename T> void vvprint(vector<vector<T>> vv) {
  REP(i, SIZE(vv)) {
    REP(j, SIZE(vv[i])) { cerr << vv[i][j] << " "; }
    cerr << endl;
  }
}

template <typename Iterator>
inline bool next_combination(const Iterator first, Iterator k,
                             const Iterator last) {
  /* Credits: Thomas Draper */
  if ((first == last) || (first == k) || (last == k))
    return false;
  Iterator itr1 = first;
  Iterator itr2 = last;
  ++itr1;
  if (last == itr1)
    return false;
  itr1 = last;
  --itr1;
  itr1 = k;
  --itr2;
  while (first != itr1) {
    if (*--itr1 < *itr2) {
      Iterator j = k;
      while (!(*itr1 < *j))
        ++j;
      iter_swap(itr1, j);
      ++itr1;
      ++j;
      itr2 = k;
      rotate(itr1, j, last);
      while (last != j) {
        ++j;
        ++itr2;
      }
      rotate(k, itr2, last);
      return true;
    }
  }
  rotate(first, k, last);
  return false;
}

inline double get_time_sec(void) {
  return static_cast<double>(chrono::duration_cast<chrono::nanoseconds>(
                                 chrono::steady_clock::now().time_since_epoch())
                                 .count()) /
         1000000000;
}

template <typename T> T gcd(T a, T b) {
  if (a > b)
    swap(a, b);
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}

template <typename T> T lcm(T a, T b) { return (a / gcd(a, b)) * b; }

template <typename T> map<T, T> prime_list(T n) {
  map<T, T> ret;
  for (T i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret[i] = 0;
      while (n % i == 0) {
        n /= i;
        ret[i]++;
      }
    }
  }
  if (n != 1)
    ret[n]++;
  return ret;
}

#define MOD 998244353

LL mypow(LL a, LL n) {
  if (n == 0)
    return 1;
  if (n == 1)
    return a % MOD;
  if (n % 2 == 1)
    return (a * mypow(a, n - 1)) % MOD;
  LL t = mypow(a, n / 2);
  return (t * t) % MOD;
}

LL mycomb(LL n, LL k) {
  if (n == 0 || n == k)
    return 1;
  LL x = 1, y = 1;
  REP(i, k) {
    x = x * (n - i) % MOD;
    y = y * (i + 1) % MOD;
  }
  return x * mypow(y, MOD - 2) % MOD;
}

#define INF 1e8

int main(void) {
  int n, m, k;
  cin >> n >> m >> k;
  VLL dp(n);
  dp[0] = m;
  FOR(i, 1, n) dp[i] = (dp[i - 1] * (m - 1)) % MOD;
  reverse(ALL(dp));
  REP(i, k + 1) {
    dp[i] *= mycomb(n - 1, i);
    dp[i] %= MOD;
  }
  // vprint(dp);
  LL ans = 0;
  REP(i, k + 1) {
    ans += dp[i];
    ans %= MOD;
  }
  cout << ans << endl;
}