Problem p03232 (C++)

Buggy submission (status: Runtime Error):
/*
    _____
  .'     '.
 /  0   0  \
|     ^     |
|  \     /  |
 \  '---'  /
  '._____.'
*/
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

template <typename T>
using ordered_set =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
random_device(rd);
mt19937 rng(rd());

template <class T> void readi(T &x) {
  T input = 0;
  bool negative = false;
  char c = ' ';
  while (c < '-') {
    c = getchar();
  }
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  while (c >= '0') {
    input = input * 10 + (c - '0');
    c = getchar();
  }
  if (negative) {
    input = -input;
  }
  x = input;
}
template <class T> void printi(T output) {
  if (output == 0) {
    putchar('0');
    return;
  }
  if (output < 0) {
    putchar('-');
    output = -output;
  }
  int aout[20];
  int ilen = 0;
  while (output) {
    aout[ilen] = ((output % 10));
    output /= 10;
    ilen++;
  }
  for (int i = ilen - 1; i >= 0; i--) {
    putchar(aout[i] + '0');
  }
  return;
}
template <class T> void ckmin(T &a, T b) { a = min(a, b); }
template <class T> void ckmax(T &a, T b) { a = max(a, b); }
long long expo(long long a, long long e, long long mod) {
  return ((e == 0)
              ? 1
              : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template <class T, class U> T nmod(T &x, U mod) {
  if (x >= mod)
    x -= mod;
}
template <class T> T gcd(T a, T b) { return (b ? gcd(b, a % b) : a); }
template <class T> T randomize(T mod) {
  return (uniform_int_distribution<T>(0, mod - 1))(rng);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;
#define sz(x) ((int)(x.size()))

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 1013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;

int N;
ll arr[MAXN];
ll fact[MAXN], ifact[MAXN];
// ll grid[MAXN][MAXN];
ll stirling[MAXN], coef[MAXN];
ll modinv[MAXN];
ll ans;

int32_t main() {
  ios_base::sync_with_stdio(0);
  // cout << fixed << setprecision(10);
  // cerr << fixed << setprecision(10);
  // freopen ("file.in", "r", stdin);
  // freopen ("file.out", "w", stdout);
  cin >> N;
  fact[0] = 1;
  for (int i = 1; i <= N; i++) {
    fact[i] = fact[i - 1] * i % INF;
  }
  ifact[N] = expo(fact[N], INF - 2, INF);
  for (int i = N - 1; i >= 0; i--) {
    ifact[i] = ifact[i + 1] * (i + 1) % INF;
  }
  for (int i = 1; i <= N; i++) {
    modinv[i] = expo(i, INF - 2, INF);
  }
  for (int i = 0; i < N; i++) {
    cin >> arr[i];
  }
  // grid[1][0] = 1;
  // for (int i = 2; i <= N; i++)
  // {
  // 	grid[i][0] = grid[i - 1][0] * i + fact[i] * expo(i, INF - 2, INF);
  // grid[i][0] %= INF; 	grid[i][i - 1] = grid[i][0]; 	for (int j = 1; j < i - 1;
  // j++)
  // 	{
  // 		grid[i][j] = grid[j + 1][j] * fact[i] % INF * ifact[j + 1] %
  // INF;
  // 		// cerr << grid[i][j] << ' ';
  // 		for (int k = 2; k <= i - j; k++)
  // 		{
  // 			grid[i][j] += fact[i] * expo(k, INF - 2, INF);
  // 		}
  // 		grid[i][j] %= INF;
  // 		// cerr << grid[i][j] << ' ';
  // 	}
  // 	// cerr << endl;
  // }
  stirling[1] = 1;
  for (int i = 2; i <= N; i++) {
    stirling[i] = stirling[i - 1] * i % INF + fact[i - 1] % INF;
    nmod(stirling[i], INF);
  }
  coef[0] = stirling[N];
  coef[N - 1] = stirling[N];
  ll sum = 0;
  for (int j = N - 2; j > 0; j--) {
    coef[j] = stirling[j + 1] * fact[N] % INF * ifact[j + 1] % INF;
    sum += fact[N] * modinv[N - j] % INF;
    nmod(sum, INF);
    coef[j] += sum;
    nmod(coef[j], INF);
    // for (int k = 2; k <= N - j; k++)
    // {
    // 	coef[j] += fact[N] * modinv[k]; coef[j] %= INF;
    // }
  }
  for (int i = 0; i < N; i++) {
    ans += coef[i] * arr[i] % INF;
    nmod(ans, INF);
  }
  cout << ans << '\n';
  // cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms"
  // << endl;
  return 0;
}


Fixed submission:
/*
    _____
  .'     '.
 /  0   0  \
|     ^     |
|  \     /  |
 \  '---'  /
  '._____.'
*/
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

template <typename T>
using ordered_set =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
random_device(rd);
mt19937 rng(rd());

template <class T> void readi(T &x) {
  T input = 0;
  bool negative = false;
  char c = ' ';
  while (c < '-') {
    c = getchar();
  }
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  while (c >= '0') {
    input = input * 10 + (c - '0');
    c = getchar();
  }
  if (negative) {
    input = -input;
  }
  x = input;
}
template <class T> void printi(T output) {
  if (output == 0) {
    putchar('0');
    return;
  }
  if (output < 0) {
    putchar('-');
    output = -output;
  }
  int aout[20];
  int ilen = 0;
  while (output) {
    aout[ilen] = ((output % 10));
    output /= 10;
    ilen++;
  }
  for (int i = ilen - 1; i >= 0; i--) {
    putchar(aout[i] + '0');
  }
  return;
}
template <class T> void ckmin(T &a, T b) { a = min(a, b); }
template <class T> void ckmax(T &a, T b) { a = max(a, b); }
long long expo(long long a, long long e, long long mod) {
  return ((e == 0)
              ? 1
              : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template <class T, class U> T nmod(T &x, U mod) {
  if (x >= mod)
    x -= mod;
}
template <class T> T gcd(T a, T b) { return (b ? gcd(b, a % b) : a); }
template <class T> T randomize(T mod) {
  return (uniform_int_distribution<T>(0, mod - 1))(rng);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;
#define sz(x) ((int)(x.size()))

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;

int N;
ll arr[MAXN];
ll fact[MAXN], ifact[MAXN];
// ll grid[MAXN][MAXN];
ll stirling[MAXN], coef[MAXN];
ll modinv[MAXN];
ll ans;

int32_t main() {
  ios_base::sync_with_stdio(0);
  // cout << fixed << setprecision(10);
  // cerr << fixed << setprecision(10);
  // freopen ("file.in", "r", stdin);
  // freopen ("file.out", "w", stdout);
  cin >> N;
  fact[0] = 1;
  for (int i = 1; i <= N; i++) {
    fact[i] = fact[i - 1] * i % INF;
  }
  ifact[N] = expo(fact[N], INF - 2, INF);
  for (int i = N - 1; i >= 0; i--) {
    ifact[i] = ifact[i + 1] * (i + 1) % INF;
  }
  for (int i = 1; i <= N; i++) {
    modinv[i] = expo(i, INF - 2, INF);
  }
  for (int i = 0; i < N; i++) {
    cin >> arr[i];
  }
  // grid[1][0] = 1;
  // for (int i = 2; i <= N; i++)
  // {
  // 	grid[i][0] = grid[i - 1][0] * i + fact[i] * expo(i, INF - 2, INF);
  // grid[i][0] %= INF; 	grid[i][i - 1] = grid[i][0]; 	for (int j = 1; j < i - 1;
  // j++)
  // 	{
  // 		grid[i][j] = grid[j + 1][j] * fact[i] % INF * ifact[j + 1] %
  // INF;
  // 		// cerr << grid[i][j] << ' ';
  // 		for (int k = 2; k <= i - j; k++)
  // 		{
  // 			grid[i][j] += fact[i] * expo(k, INF - 2, INF);
  // 		}
  // 		grid[i][j] %= INF;
  // 		// cerr << grid[i][j] << ' ';
  // 	}
  // 	// cerr << endl;
  // }
  stirling[1] = 1;
  for (int i = 2; i <= N; i++) {
    stirling[i] = stirling[i - 1] * i % INF + fact[i - 1] % INF;
    nmod(stirling[i], INF);
  }
  coef[0] = stirling[N];
  coef[N - 1] = stirling[N];
  ll sum = 0;
  for (int j = N - 2; j > 0; j--) {
    coef[j] = stirling[j + 1] * fact[N] % INF * ifact[j + 1] % INF;
    sum += fact[N] * modinv[N - j] % INF;
    nmod(sum, INF);
    coef[j] += sum;
    nmod(coef[j], INF);
    // for (int k = 2; k <= N - j; k++)
    // {
    // 	coef[j] += fact[N] * modinv[k]; coef[j] %= INF;
    // }
  }
  for (int i = 0; i < N; i++) {
    ans += coef[i] * arr[i] % INF;
    nmod(ans, INF);
  }
  cout << ans << '\n';
  // cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms"
  // << endl;
  return 0;
}