Problem p03065 (C++)

Buggy submission (status: Runtime Error):
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC target ("avx2")
// #pragma GCC optimization ("unroll-loops")

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
using namespace __gnu_pbds;
template <class T>
using Tree =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

const long double PI = 4 * atan(1);

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define f1r(i, a, b) for (int i = (a); i < (b); ++i)
#define f0r(i, a) f1r(i, 0, a)
#define trav(a, x) for (auto &a : x)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)(x).size()
#define all(x) x.begin(), x.end()
#define rall(x) rbegin(x), rend(x)
#define resz resize
#define rsz resize
#define ins insert

template <typename A, typename B>
ostream &operator<<(ostream &cout, pair<A, B> const &p) {
  return cout << "(" << p.f << ", " << p.s << ")";
}
template <typename A> ostream &operator<<(ostream &cout, vector<A> const &v) {
  cout << "[";
  for (int i = 0; i < v.size(); i++) {
    if (i)
      cout << ", ";
    cout << v[i];
  }
  return cout << "]";
}

template <class T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

namespace input {
template <class T> void re(complex<T> &x);
template <class T1, class T2> void re(pair<T1, T2> &p);
template <class T> void re(vector<T> &a);
template <class T, size_t SZ> void re(array<T, SZ> &a);
template <class T> void re(T &x) { cin >> x; }
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
void re(ld &x) {
  string t;
  re(t);
  x = stold(t);
}
template <class T, class... Ts> void re(T &t, Ts &...ts) {
  re(t);
  re(ts...);
}
template <class T> void re(complex<T> &x) {
  T a, b;
  re(a, b);
  x = cd(a, b);
}
template <class T1, class T2> void re(pair<T1, T2> &p) { re(p.f, p.s); }
template <class T> void re(vector<T> &a) { F0R(i, sz(a)) re(a[i]); }
template <class T, size_t SZ> void re(array<T, SZ> &a) { F0R(i, SZ) re(a[i]); }
} // namespace input

using namespace input;

namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char *x) { cout << x; }
void pr(const string &x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T> void pr(const complex<T> &x) { cout << x; }
template <class T1, class T2> void pr(const pair<T1, T2> &x);
template <class T> void pr(const T &x);
template <class T, class... Ts> void pr(const T &t, const Ts &...ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2> void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T> void pr(const T &x) {
  pr("{"); // const iterator needed for vector<bool>
  bool fst = 1;
  for (const auto &a : x)
    pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}
void ps() { pr("\n"); } // print w/ spaces
template <class T, class... Ts> void ps(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(" ");
  ps(ts...);
}
void pc() { pr("]\n"); } // debug w/ commas
template <class T, class... Ts> void pc(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(", ");
  pc(ts...);
}
#ifdef TQIAN
#define dbg(x...) pr("[", #x, "] = ["), pc(x);
#else
#define dbg(x...) 0
#endif
} // namespace output

using namespace output;

namespace io {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  cin.sync_with_stdio(0);
  cin.tie(0); // fast I/O
  // cin.exceptions(cin.failbit); // ex. throws exception when you try to read
  // letter into int
  if (sz(s)) {
    setIn(s + ".in"), setOut(s + ".out");
  } // for USACO
}
} // namespace io

using namespace io;
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

const int MOD = 1e9 + 7;

typedef decay<decltype(MOD)>::type T;
struct mi {
  T val;
  explicit operator T() const { return val; }
  mi() { val = 0; }
  mi(const ll &v) {
    val = (-MOD <= v && v <= MOD) ? v : v % MOD;
    if (val < 0)
      val += MOD;
  }
  friend ostream &operator<<(ostream &os, const mi &a) { return os << a.val; }
  friend void pr(const mi &a) { pr(a.val); }
  friend void re(mi &a) {
    ll x;
    re(x);
    a = mi(x);
  }
  friend bool operator==(const mi &a, const mi &b) { return a.val == b.val; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.val < b.val; }
  mi operator-() const { return mi(-val); }
  mi &operator+=(const mi &m) {
    if ((val += m.val) >= MOD)
      val -= MOD;
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((val -= m.val) < 0)
      val += MOD;
    return *this;
  }
  mi &operator*=(const mi &m) {
    val = (ll)val * m.val % MOD;
    return *this;
  }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a != 0);
    return pow(a, MOD - 2);
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
};

typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
const ll INF = 1e18;
vl getPrime(ll n) {
  set<ll> primes;
  while (n % 2 == 0) {
    primes.insert(2);
    n = n / 2;
  }
  for (ll i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      primes.insert(i);
      n = n / i;
    }
  }
  if (n > 2)
    primes.insert(n);
  vl ret;
  for (int x : primes)
    ret.eb(x);
  return ret;
}
void solve_easy(int n, vl v) {
  int lead = -1;
  f0r(i, n + 1) {
    if (v[i] != 0) {
      lead = v[i];
      break;
    }
  }
  vl pri = getPrime(abs(lead));
  vi res;
  for (int p : pri) {
    vi use(n + 1);
    f0r(i, n + 1) {
      use[i % (p - 1)] += ((v[i] % p + p) % p);
      use[i % (p - 1)] %= p;
    }
    f0r(i, n + 1) if (use[i] % p) goto finish;
    res.eb(p);
  finish:
    continue;
  }
  for (auto x : res)
    ps(x);
}
ll modpow(ll base, ll exp, ll mod) {
  ll res = 1;
  while (exp) {
    if (exp % 2)
      res *= base;
    res %= mod;
    base *= base;
    base %= mod;
    exp >>= 1;
  }
  return res;
}
const ll p1 = 179424673;
const ll p2 = 179424697;
bool eval(vl &v, ll x, ll mod) {
  ll sum = 0;
  f0r(i, sz(v)) {
    ll ad = modpow(x, i, mod);
    ad *= v[i];
    ad %= mod;
    sum += ad;
  }
  if (sum == 0)
    return false;
  return true;
}
ll eval1(vl &v, ll x, ll mod) {
  ll sum = 0;
  f0r(i, sz(v)) {
    ll ad = modpow(x, i, mod);
    ad *= v[i];
    ad %= mod;
    sum += ad;
  }
  return sum;
}
bool check_good(vl &v, ll x) {
  if (eval(v, x, p1) || eval(v, x, p2))
    return true;
  return false;
}
vl sieve(int n) {
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p)
        prime[i] = false;
    }
  }
  vl ret;
  // Print all prime numbers
  for (int p = 2; p <= n; p++)
    if (prime[p])
      ret.eb(p);
  return ret;
}
int main() {
  setIn("temp.in");
  int n;
  re(n);
  vl v(n + 1);
  f0r(i, n + 1) re(v[i]);
  reverse(all(v));
  if (v[0] != 0) {
    solve_easy(n, v);
    return 0;
  }
  reverse(all(v));
  while (v.back() == 0)
    v.pop_back();
  n = sz(v) - 1;
  reverse(all(v));
  vl tmp = sieve(n + 4);
  set<ll> pri;
  for (auto x : tmp)
    pri.insert(x);
  for (auto x : v) {
    if (x == 0)
      continue;
    tmp = getPrime(abs(x));
    for (auto y : tmp)
      pri.insert(y);
  }
  set<ll> res;
  vl nonzero;
  for (auto x : v)
    nonzero.eb(abs(x));
  for (ll p : pri) {
    if (p >= n + 5) {
      for (auto y : nonzero) {
        if (y % p != 0)
          goto what;
      }
      res.insert(p);
    what:
      continue;
      continue;
    }
    vl use(n + 1);
    f0r(i, n + 1) {
      use[i % (p - 1)] += ((v[i] % p + p) % p);
      use[i % (p - 1)] %= p;
    }
    f0r(i, n + 1) if (use[i] % p) goto finish;
    res.insert(p);
  finish:
    continue;
  }
  for (auto x : res)
    ps(x);
  return 0;
}


Fixed submission:
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC target ("avx2")
// #pragma GCC optimization ("unroll-loops")

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
using namespace __gnu_pbds;
template <class T>
using Tree =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

const long double PI = 4 * atan(1);

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define f1r(i, a, b) for (int i = (a); i < (b); ++i)
#define f0r(i, a) f1r(i, 0, a)
#define trav(a, x) for (auto &a : x)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)(x).size()
#define all(x) x.begin(), x.end()
#define rall(x) rbegin(x), rend(x)
#define resz resize
#define rsz resize
#define ins insert

template <typename A, typename B>
ostream &operator<<(ostream &cout, pair<A, B> const &p) {
  return cout << "(" << p.f << ", " << p.s << ")";
}
template <typename A> ostream &operator<<(ostream &cout, vector<A> const &v) {
  cout << "[";
  for (int i = 0; i < v.size(); i++) {
    if (i)
      cout << ", ";
    cout << v[i];
  }
  return cout << "]";
}

template <class T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

namespace input {
template <class T> void re(complex<T> &x);
template <class T1, class T2> void re(pair<T1, T2> &p);
template <class T> void re(vector<T> &a);
template <class T, size_t SZ> void re(array<T, SZ> &a);
template <class T> void re(T &x) { cin >> x; }
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
void re(ld &x) {
  string t;
  re(t);
  x = stold(t);
}
template <class T, class... Ts> void re(T &t, Ts &...ts) {
  re(t);
  re(ts...);
}
template <class T> void re(complex<T> &x) {
  T a, b;
  re(a, b);
  x = cd(a, b);
}
template <class T1, class T2> void re(pair<T1, T2> &p) { re(p.f, p.s); }
template <class T> void re(vector<T> &a) { F0R(i, sz(a)) re(a[i]); }
template <class T, size_t SZ> void re(array<T, SZ> &a) { F0R(i, SZ) re(a[i]); }
} // namespace input

using namespace input;

namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char *x) { cout << x; }
void pr(const string &x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T> void pr(const complex<T> &x) { cout << x; }
template <class T1, class T2> void pr(const pair<T1, T2> &x);
template <class T> void pr(const T &x);
template <class T, class... Ts> void pr(const T &t, const Ts &...ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2> void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T> void pr(const T &x) {
  pr("{"); // const iterator needed for vector<bool>
  bool fst = 1;
  for (const auto &a : x)
    pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}
void ps() { pr("\n"); } // print w/ spaces
template <class T, class... Ts> void ps(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(" ");
  ps(ts...);
}
void pc() { pr("]\n"); } // debug w/ commas
template <class T, class... Ts> void pc(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(", ");
  pc(ts...);
}
#ifdef TQIAN
#define dbg(x...) pr("[", #x, "] = ["), pc(x);
#else
#define dbg(x...) 0
#endif
} // namespace output

using namespace output;

namespace io {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  cin.sync_with_stdio(0);
  cin.tie(0); // fast I/O
  // cin.exceptions(cin.failbit); // ex. throws exception when you try to read
  // letter into int
  if (sz(s)) {
    setIn(s + ".in"), setOut(s + ".out");
  } // for USACO
}
} // namespace io

using namespace io;
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

const int MOD = 1e9 + 7;

typedef decay<decltype(MOD)>::type T;
struct mi {
  T val;
  explicit operator T() const { return val; }
  mi() { val = 0; }
  mi(const ll &v) {
    val = (-MOD <= v && v <= MOD) ? v : v % MOD;
    if (val < 0)
      val += MOD;
  }
  friend ostream &operator<<(ostream &os, const mi &a) { return os << a.val; }
  friend void pr(const mi &a) { pr(a.val); }
  friend void re(mi &a) {
    ll x;
    re(x);
    a = mi(x);
  }
  friend bool operator==(const mi &a, const mi &b) { return a.val == b.val; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.val < b.val; }
  mi operator-() const { return mi(-val); }
  mi &operator+=(const mi &m) {
    if ((val += m.val) >= MOD)
      val -= MOD;
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((val -= m.val) < 0)
      val += MOD;
    return *this;
  }
  mi &operator*=(const mi &m) {
    val = (ll)val * m.val % MOD;
    return *this;
  }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a != 0);
    return pow(a, MOD - 2);
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
};

typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
const ll INF = 1e18;
vl getPrime(ll n) {
  set<ll> primes;
  while (n % 2 == 0) {
    primes.insert(2);
    n = n / 2;
  }
  for (ll i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      primes.insert(i);
      n = n / i;
    }
  }
  if (n > 2)
    primes.insert(n);
  vl ret;
  for (int x : primes)
    ret.eb(x);
  return ret;
}
void solve_easy(int n, vl v) {
  int lead = -1;
  f0r(i, n + 1) {
    if (v[i] != 0) {
      lead = v[i];
      break;
    }
  }
  vl pri = getPrime(abs(lead));
  vi res;
  for (int p : pri) {
    vi use(n + 1);
    f0r(i, n + 1) {
      use[i % (p - 1)] += ((v[i] % p + p) % p);
      use[i % (p - 1)] %= p;
    }
    f0r(i, n + 1) if (use[i] % p) goto finish;
    res.eb(p);
  finish:
    continue;
  }
  for (auto x : res)
    ps(x);
}
ll modpow(ll base, ll exp, ll mod) {
  ll res = 1;
  while (exp) {
    if (exp % 2)
      res *= base;
    res %= mod;
    base *= base;
    base %= mod;
    exp >>= 1;
  }
  return res;
}
const ll p1 = 179424673;
const ll p2 = 179424697;
bool eval(vl &v, ll x, ll mod) {
  ll sum = 0;
  f0r(i, sz(v)) {
    ll ad = modpow(x, i, mod);
    ad *= v[i];
    ad %= mod;
    sum += ad;
  }
  if (sum == 0)
    return false;
  return true;
}
ll eval1(vl &v, ll x, ll mod) {
  ll sum = 0;
  f0r(i, sz(v)) {
    ll ad = modpow(x, i, mod);
    ad *= v[i];
    ad %= mod;
    sum += ad;
  }
  return sum;
}
bool check_good(vl &v, ll x) {
  if (eval(v, x, p1) || eval(v, x, p2))
    return true;
  return false;
}
vl sieve(int n) {
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p)
        prime[i] = false;
    }
  }
  vl ret;
  // Print all prime numbers
  for (int p = 2; p <= n; p++)
    if (prime[p])
      ret.eb(p);
  return ret;
}
int main() {
  //    setIn("temp.in");
  int n;
  re(n);
  vl v(n + 1);
  f0r(i, n + 1) re(v[i]);
  reverse(all(v));
  if (v[0] != 0) {
    solve_easy(n, v);
    return 0;
  }
  reverse(all(v));
  while (v.back() == 0)
    v.pop_back();
  n = sz(v) - 1;
  reverse(all(v));
  vl tmp = sieve(n + 4);
  set<ll> pri;
  for (auto x : tmp)
    pri.insert(x);
  for (auto x : v) {
    if (x == 0)
      continue;
    tmp = getPrime(abs(x));
    for (auto y : tmp)
      pri.insert(y);
  }
  set<ll> res;
  vl nonzero;
  for (auto x : v)
    nonzero.eb(abs(x));
  for (ll p : pri) {
    if (p >= n + 5) {
      for (auto y : nonzero) {
        if (y % p != 0)
          goto what;
      }
      res.insert(p);
    what:
      continue;
      continue;
    }
    vl use(n + 1);
    f0r(i, n + 1) {
      use[i % (p - 1)] += ((v[i] % p + p) % p);
      use[i % (p - 1)] %= p;
    }
    f0r(i, n + 1) if (use[i] % p) goto finish;
    res.insert(p);
  finish:
    continue;
  }
  for (auto x : res)
    ps(x);
  return 0;
}