Problem p03083 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
// #define int ll
// #define int __int128
// #define ll __int128
// typedef __int128 long long;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;
typedef complex<double> base;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \
  if (false)                                                                   \
  cerr
#endif

const double PI = 2 * acos(0.0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);

#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\n\n\n\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
}

const int N = 1e5 + 100;
const ll M = 1e9 + 7;

ll pw(ll a, ll n = M - 2) {
  ll ret = 1;
  while (n) {
    if (n & 1)
      ret = ret * a % M;
    a = a * a % M;
    n >>= 1;
  }
  return ret;
}

ll b, w;

ll fact[N], inv[N];

ll nCr(ll n, ll k) {
  if (k > n || k < 0)
    return 0;
  return fact[n] * inv[k] % M * inv[n - k] % M;
}

ll pref_q[N];

ll suf_p[N];

void smain() {

  fact[0] = 1;
  for (int i = 1; i < N; ++i) {
    fact[i] = fact[i - 1] * i % M;
  }

  inv[N - 1] = pw(fact[N - 1]);
  for (int i = N - 2; i >= 0; --i) {
    inv[i] = inv[i + 1] * (i + 1) % M;
  }

  cin >> b >> w;
  ll n = b + w;

  for (ll j = 2; j <= n; ++j) {
    ll cur = pw(pw(2, j - 1)) * nCr(j - 1 - 1, w - 1) % M;
    pref_q[j] = (pref_q[j - 1] + cur) % M;
  }

  for (ll j = n - 2; j >= 0; --j) {
    ll cur = nCr(j + 1 - 2, b - 2) + nCr(j + 1 - 2, w - 1);
    cur %= M;
    cur = cur * pw(pw(2, j + 1)) % M;
    suf_p[j] = (cur + suf_p[j + 1]) % M;
  }

  for (ll j = 1; j <= n; ++j) {
    ll q = pref_q[j];
    ll p = suf_p[j];
    ll cur = nCr(j - 1, b - 1) * pw(pw(2, j)) % M;
    if (j == n)
      cur = 0;
    p = (p + cur) % M;
    p = (p + q) % M;
    cout << p << '\n';
  }
}

Fixed submission:
#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
// #define int ll
// #define int __int128
// #define ll __int128
// typedef __int128 long long;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;
typedef complex<double> base;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \
  if (false)                                                                   \
  cerr
#endif

const double PI = 2 * acos(0.0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);

#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\n\n\n\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
}

const int N = 4e5 + 100;
const ll M = 1e9 + 7;

ll pw(ll a, ll n = M - 2) {
  ll ret = 1;
  while (n) {
    if (n & 1)
      ret = ret * a % M;
    a = a * a % M;
    n >>= 1;
  }
  return ret;
}

ll b, w;

ll fact[N], inv[N];

ll nCr(ll n, ll k) {
  if (k > n || k < 0)
    return 0;
  return fact[n] * inv[k] % M * inv[n - k] % M;
}

ll pref_q[N];

ll suf_p[N];

void smain() {

  fact[0] = 1;
  for (int i = 1; i < N; ++i) {
    fact[i] = fact[i - 1] * i % M;
  }

  inv[N - 1] = pw(fact[N - 1]);
  for (int i = N - 2; i >= 0; --i) {
    inv[i] = inv[i + 1] * (i + 1) % M;
  }

  cin >> b >> w;
  ll n = b + w;

  for (ll j = 2; j <= n; ++j) {
    ll cur = pw(pw(2, j - 1)) * nCr(j - 1 - 1, w - 1) % M;
    pref_q[j] = (pref_q[j - 1] + cur) % M;
  }

  for (ll j = n - 2; j >= 0; --j) {
    ll cur = nCr(j + 1 - 2, b - 2) + nCr(j + 1 - 2, w - 1);
    cur %= M;
    cur = cur * pw(pw(2, j + 1)) % M;
    suf_p[j] = (cur + suf_p[j + 1]) % M;
  }

  for (ll j = 1; j <= n; ++j) {
    ll q = pref_q[j];
    ll p = suf_p[j];
    ll cur = nCr(j - 1, b - 1) * pw(pw(2, j)) % M;
    if (j == n)
      cur = 0;
    p = (p + cur) % M;
    p = (p + q) % M;
    cout << p << '\n';
  }
}