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

#include "bits/stdc++.h"
using namespace std;

#define rep(i, n) for (int(i) = 0; (i) < (n); (i)++)
#define rep3(i, m, n) for (int(i) = m; (i) <= (n); (i)++)
#define rep3rev(i, m, n) for (int(i) = m; (i) >= (n); (i)--)
#define all(a) (a.begin()), (a.end())
#define rall(a) (a.rbegin()), (a.rend())
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define mp make_pair

using ll = long long;
using vll = vector<ll>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using P = pair<int, int>;

/*** MOD CALCULATION ***/

const int MOD = 998244353;
const int MAX = 200100;

ll addM(ll a, ll b) { return (a + b) % MOD; }

ll mulM(ll a, ll b) {
  ll temp = (a * b) % MOD;
  while (temp < 0) {
    temp += MOD;
  }
  return temp;
}

ll powM(ll a, ll b) {
  if (b == 0)
    return 1;
  else if (b == 1)
    return a % MOD;
  else if (b % 2 == 0)
    return mulM(powM(a, b / 2), powM(a, b / 2));
  else
    return mulM(a, mulM(powM(a, (b - 1) / 2), powM(a, (b - 1) / 2)));
}

// b^{-1} = b^{p-2} (mod p)
// a/b = a*b^{p-2} (mod p)
ll divM(ll a, ll b) { return mulM(a, powM(b, MOD - 2)); }

// n!, (n!)^{-1} のテーブル作成
ll fac[MAX], finv[MAX], inv[MAX];
void COMBinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  rep3(i, 2, MAX - 1) {
    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
ll COMB(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;
}

/*** MOD CALCULATION ここまで ***/

void Main() {
  ll n, m, k;
  cin >> n >> m >> k;

  COMBinit();

  ll ans = 0;
  rep(i, k + 1) {
    ll temp = m;
    temp = mulM(temp, powM(m - 1, n - i - 1));
    temp = mulM(temp, COMB(n - 1, i));
    ans = addM(ans, temp);
    // cout << ans << endl;
  }

  cout << ans << endl;
  return;
}

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}


Error: TLE

Fixed submission:

#include "bits/stdc++.h"
using namespace std;

#define rep(i, n) for (int(i) = 0; (i) < (n); (i)++)
#define rep3(i, m, n) for (int(i) = m; (i) <= (n); (i)++)
#define rep3rev(i, m, n) for (int(i) = m; (i) >= (n); (i)--)
#define all(a) (a.begin()), (a.end())
#define rall(a) (a.rbegin()), (a.rend())
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define mp make_pair

using ll = long long;
using vll = vector<ll>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using P = pair<int, int>;

/*** MOD CALCULATION ***/

const int MOD = 998244353;
const int MAX = 200100;

ll addM(ll a, ll b) { return (a + b) % MOD; }

ll mulM(ll a, ll b) {
  ll temp = (a * b) % MOD;
  while (temp < 0) {
    temp += MOD;
  }
  return temp;
}

ll powM(ll a, ll b) {
  if (b == 0)
    return 1;
  else if (b == 1)
    return a % MOD;
  else if (b % 2 == 0)
    return mulM(powM(a, b / 2), powM(a, b / 2));
  else
    return mulM(a, mulM(powM(a, (b - 1) / 2), powM(a, (b - 1) / 2)));
}

// b^{-1} = b^{p-2} (mod p)
// a/b = a*b^{p-2} (mod p)
ll divM(ll a, ll b) { return mulM(a, powM(b, MOD - 2)); }

// n!, (n!)^{-1} のテーブル作成
ll fac[MAX], finv[MAX], inv[MAX];
void COMBinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  rep3(i, 2, MAX - 1) {
    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
ll COMB(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;
}

/*** MOD CALCULATION ここまで ***/

void Main() {
  ll n, m, k;
  cin >> n >> m >> k;

  COMBinit();

  ll ans = 0;
  rep(i, k + 1) {
    ll temp = m;
    rep(j, n - i - 1) temp = mulM(temp, m - 1);
    ll c = COMB(n - 1, i);
    temp = mulM(temp, c);
    ans = addM(ans, temp);
    // cout << ans << endl;
  }

  cout << ans << endl;
  return;
}

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}