Problem p02769 (C++)

Buggy submission (status: Runtime Error):
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep0(i, n) for (int i = 0; i <= (int)(n); ++i)
#define rep1(i, n) for (int i = 1; i <= (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
template <typename T> using Graph = vector<vector<T>>;
template <typename T> using Spacial = vector<vector<vector<T>>>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int MOD = 1e9 + 7;
const int MOD2 = 998244353;
const double EPS = 1e-9;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

template <typename T> struct is_pair : false_type {};
template <typename T1, typename T2> struct is_pair<pair<T1, T2>> : true_type {};
template <typename T> struct is_vector : false_type {};
template <typename T> struct is_vector<vector<T>> : true_type {};

template <typename T1, typename T2>
istream &operator>>(istream &istr, pair<T1, T2> &p) {
  istr >> p.first >> p.second;
  return istr;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &ostr, const pair<T1, T2> &p) {
  ostr << p.first << " " << p.second;
  return ostr;
}
template <typename T> ostream &operator<<(ostream &ostr, const vector<T> &vec) {
  if (vec.empty())
    return ostr;
  bool vp = is_vector<T>() || is_pair<T>();
  ostr << vec.front();
  for (auto itr = ++vec.begin(); itr != vec.end(); ++itr) {
    ostr << (vp ? "\n" : " ") << *itr;
  }
  return ostr;
}

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

int modpow(int a, long long n, int mod = MOD) {
  int ret = 1;
  do {
    if (n & 1)
      ret = 1LL * ret * a % mod;
    a = 1LL * a * a % mod;
  } while (n >>= 1);
  return ret;
}

template <typename T> T GCD(T a, T b) { return b ? GCD(b, a % b) : a; }
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }

template <typename T1, typename T2>
bool CompareBySecond(pair<T1, T2> a, pair<T1, T2> b) {
  return a.second != b.second ? a.second < b.second : a.first < b.first;
}
template <typename T> bool CompareBySlope(pair<T, T> a, pair<T, T> b) {
  // counterclockwise from 12 o'clock direction
  if (a.first * b.first < 0)
    return a.first < b.first;
  if (a.first == 0)
    return a.second >= 0 || b.first > 0;
  if (b.first == 0)
    return b.second < 0 && a.first < 0;
  return a.second * b.first < a.first * b.second;
}

/* -------- <templates end> -------- */

vector<long long> fac, finv, inv;

void com_init(int MAX) {
  ++MAX;
  fac.resize(MAX);
  fac[0] = fac[1] = 1;
  finv.resize(MAX);
  finv[0] = finv[1] = 1;
  inv.resize(MAX);
  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;
  }
}

long long combination(int n, int r) {
  if (n < r)
    return 0;
  if (n < 0 || r < 0)
    return 0;
  return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
}

void solve() {
  int n, k;
  cin >> n >> k;
  com_init(n);

  if (k >= n - 1) {
    cout << combination(2 * n - 1, n) << endl;
    return;
  }

  int ans = 1;
  rep1(i, k) {
    (ans += combination(n, i) * combination(n - 1, i) % MOD) %= MOD;
  }
  cout << ans << endl;
}

/* -------- <programs end> -------- */

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  solve();
  return 0;
}


Fixed submission:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep0(i, n) for (int i = 0; i <= (int)(n); ++i)
#define rep1(i, n) for (int i = 1; i <= (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
template <typename T> using Graph = vector<vector<T>>;
template <typename T> using Spacial = vector<vector<vector<T>>>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int MOD = 1e9 + 7;
const int MOD2 = 998244353;
const double EPS = 1e-9;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

template <typename T> struct is_pair : false_type {};
template <typename T1, typename T2> struct is_pair<pair<T1, T2>> : true_type {};
template <typename T> struct is_vector : false_type {};
template <typename T> struct is_vector<vector<T>> : true_type {};

template <typename T1, typename T2>
istream &operator>>(istream &istr, pair<T1, T2> &p) {
  istr >> p.first >> p.second;
  return istr;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &ostr, const pair<T1, T2> &p) {
  ostr << p.first << " " << p.second;
  return ostr;
}
template <typename T> ostream &operator<<(ostream &ostr, const vector<T> &vec) {
  if (vec.empty())
    return ostr;
  bool vp = is_vector<T>() || is_pair<T>();
  ostr << vec.front();
  for (auto itr = ++vec.begin(); itr != vec.end(); ++itr) {
    ostr << (vp ? "\n" : " ") << *itr;
  }
  return ostr;
}

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

int modpow(int a, long long n, int mod = MOD) {
  int ret = 1;
  do {
    if (n & 1)
      ret = 1LL * ret * a % mod;
    a = 1LL * a * a % mod;
  } while (n >>= 1);
  return ret;
}

template <typename T> T GCD(T a, T b) { return b ? GCD(b, a % b) : a; }
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }

template <typename T1, typename T2>
bool CompareBySecond(pair<T1, T2> a, pair<T1, T2> b) {
  return a.second != b.second ? a.second < b.second : a.first < b.first;
}
template <typename T> bool CompareBySlope(pair<T, T> a, pair<T, T> b) {
  // counterclockwise from 12 o'clock direction
  if (a.first * b.first < 0)
    return a.first < b.first;
  if (a.first == 0)
    return a.second >= 0 || b.first > 0;
  if (b.first == 0)
    return b.second < 0 && a.first < 0;
  return a.second * b.first < a.first * b.second;
}

/* -------- <templates end> -------- */

vector<long long> fac, finv, inv;

void com_init(int MAX) {
  ++MAX;
  fac.resize(MAX);
  fac[0] = fac[1] = 1;
  finv.resize(MAX);
  finv[0] = finv[1] = 1;
  inv.resize(MAX);
  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;
  }
}

long long combination(int n, int r) {
  if (n < r)
    return 0;
  if (n < 0 || r < 0)
    return 0;
  return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
}

void solve() {
  int n, k;
  cin >> n >> k;
  com_init(2 * n);

  if (k >= n - 1) {
    cout << combination(2 * n - 1, n) << endl;
    return;
  }

  int ans = 1;
  rep1(i, k) {
    (ans += combination(n, i) * combination(n - 1, i) % MOD) %= MOD;
  }
  cout << ans << endl;
}

/* -------- <programs end> -------- */

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  solve();
  return 0;
}