Problem p03154 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <time.h>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define all(a) a.begin(), a.end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define pb push_back
#define debug(x) cerr << #x << ':' << x << '\n'
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef complex<ld> com;
constexpr int inf = 1000000010;
constexpr ll INF = 1000000000000000010;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
template <class T, class U> inline bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class U> inline bool chmin(T &a, const U &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

constexpr ll mod = 1000000007;

vector<vector<ll>> mat_mul(vector<vector<ll>> a, vector<vector<ll>> b) {
  int n = a.size();
  vector<vector<ll>> ans(n, vector<ll>(n));
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        ans[i][j] += a[i][k] * b[k][j];
        ans[i][j] %= mod;
      }
    }
  }
  return ans;
}

vector<vector<ll>> mat_pow(vector<vector<ll>> a, ll b) {
  int n = a.size();
  vector<vector<ll>> ans(n, vector<ll>(n));
  for (int i = 0; i < n; i++)
    ans[i][i] = 1;
  while (b) {
    if (b & 1)
      ans = mat_mul(ans, a);
    a = mat_mul(a, a);
    b >>= 1;
  }
  return ans;
}

vector<ll> fac, inv, facinv;

void modcalc(int modsize) {
  fac.resize(modsize);
  inv.resize(modsize);
  facinv.resize(modsize);
  fac[0] = 1;
  fac[1] = 1;
  inv[1] = 1;
  facinv[0] = 1;
  facinv[1] = 1;
  for (ll i = 2; i < modsize; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    facinv[i] = facinv[i - 1] * inv[i] % mod;
  }
}

ll modinv(ll a) {
  a %= mod;
  if (a == 0)
    abort();
  if (a < (ll)inv.size())
    return inv[a];
  ll b = mod, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}

ll modpow(ll a, ll b, ll m = mod) {
  ll ans = 1;
  a %= m;
  while (b) {
    if (b & 1)
      ans = ans * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return ans;
}

ll modcomb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return fac[n] * facinv[k] % mod * facinv[n - k] % mod;
}

ll modperm(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return fac[n] * facinv[n - k] % mod;
}

ll modhom(ll n, ll k) {
  if (n < 0 || k < 0 || n == 0 && k > 0)
    return 0;
  if (n == 0 && k == 0)
    return 1;
  return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);
  modcalc(10000010);

  ll h, w, k;
  cin >> h >> w >> k;
  vector<vector<ll>> mat = {
      {1, 1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1}, {0, 0, 0, 1}};
  mat = mat_pow(mat, k);
  ll val = (modcomb(h + w, h) + 2 * modcomb(h + w - 2, h - 1)) % mod;
  ll ans = 0;
  ans += modcomb(h + w, h) * 2 * mat[0][1] % mod;
  ans += val * mat[0][2] % mod;
  ans += (mod + val - modcomb(h + w, h)) * mat[0][3] % mod;
  ans %= mod;
  ans *= modinv(modcomb(h + w, h));
  ans %= mod;
  ans *= modperm(h + w, k);
  ans %= mod;
  cout << ans << '\n';
}

Fixed submission:
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <time.h>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define all(a) a.begin(), a.end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define pb push_back
#define debug(x) cerr << #x << ':' << x << '\n'
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef complex<ld> com;
constexpr int inf = 1000000010;
constexpr ll INF = 1000000000000000010;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
template <class T, class U> inline bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class U> inline bool chmin(T &a, const U &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

constexpr ll mod = 1000000007;

vector<vector<ll>> mat_mul(vector<vector<ll>> a, vector<vector<ll>> b) {
  int n = a.size();
  vector<vector<ll>> ans(n, vector<ll>(n));
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        ans[i][j] += a[i][k] * b[k][j];
        ans[i][j] %= mod;
      }
    }
  }
  return ans;
}

vector<vector<ll>> mat_pow(vector<vector<ll>> a, ll b) {
  int n = a.size();
  vector<vector<ll>> ans(n, vector<ll>(n));
  for (int i = 0; i < n; i++)
    ans[i][i] = 1;
  while (b) {
    if (b & 1)
      ans = mat_mul(ans, a);
    a = mat_mul(a, a);
    b >>= 1;
  }
  return ans;
}

vector<ll> fac, inv, facinv;

void modcalc(int modsize) {
  fac.resize(modsize);
  inv.resize(modsize);
  facinv.resize(modsize);
  fac[0] = 1;
  fac[1] = 1;
  inv[1] = 1;
  facinv[0] = 1;
  facinv[1] = 1;
  for (ll i = 2; i < modsize; i++) {
    fac[i] = fac[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    facinv[i] = facinv[i - 1] * inv[i] % mod;
  }
}

ll modinv(ll a) {
  a %= mod;
  if (a == 0)
    abort();
  if (a < (ll)inv.size())
    return inv[a];
  ll b = mod, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}

ll modpow(ll a, ll b, ll m = mod) {
  ll ans = 1;
  a %= m;
  while (b) {
    if (b & 1)
      ans = ans * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return ans;
}

ll modcomb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return fac[n] * facinv[k] % mod * facinv[n - k] % mod;
}

ll modperm(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return fac[n] * facinv[n - k] % mod;
}

ll modhom(ll n, ll k) {
  if (n < 0 || k < 0 || n == 0 && k > 0)
    return 0;
  if (n == 0 && k == 0)
    return 1;
  return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);
  modcalc(20000010);

  ll h, w, k;
  cin >> h >> w >> k;
  vector<vector<ll>> mat = {
      {1, 1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1}, {0, 0, 0, 1}};
  mat = mat_pow(mat, k);
  ll val = (modcomb(h + w, h) + 2 * modcomb(h + w - 2, h - 1)) % mod;
  ll ans = 0;
  ans += modcomb(h + w, h) * 2 * mat[0][1] % mod;
  ans += val * mat[0][2] % mod;
  ans += (mod + val - modcomb(h + w, h)) * mat[0][3] % mod;
  ans %= mod;
  ans *= modinv(modcomb(h + w, h));
  ans %= mod;
  ans *= modperm(h + w, k);
  ans %= mod;
  cout << ans << '\n';
}