Problem p03065 (C++)

Buggy submission (status: Time Limit Exceeded):
// #include <bits/stdc++.h>
#include <algorithm> // min,max
#include <cmath>     // sqrt
#include <cstdlib>   // exit
#include <iostream>
#include <list>
#include <map>
#include <unordered_map>
#include <vector>
using namespace std;
#define forr(i, m, n) for (int i = (m); i <= (n); i++)
#define forv(i, m, n) for (int i = (m); i >= (n); i--)
#define forall(it, p) for (auto it = p.begin(); it != p.end(); ++it)
#define R 1000000007
#define DBG 1

#define MAXN 10002
int a[MAXN];
long c[MAXN];
int faca[MAXN];
int exaa[MAXN];
int ps[MAXN] = {
    2,    3,    5,    7,    11,   13,   17,   19,   23,   29,   31,   37,
    41,   43,   47,   53,   59,   61,   67,   71,   73,   79,   83,   89,
    97,   101,  103,  107,  109,  113,  127,  131,  137,  139,  149,  151,
    157,  163,  167,  173,  179,  181,  191,  193,  197,  199,  211,  223,
    227,  229,  233,  239,  241,  251,  257,  263,  269,  271,  277,  281,
    283,  293,  307,  311,  313,  317,  331,  337,  347,  349,  353,  359,
    367,  373,  379,  383,  389,  397,  401,  409,  419,  421,  431,  433,
    439,  443,  449,  457,  461,  463,  467,  479,  487,  491,  499,  503,
    509,  521,  523,  541,  547,  557,  563,  569,  571,  577,  587,  593,
    599,  601,  607,  613,  617,  619,  631,  641,  643,  647,  653,  659,
    661,  673,  677,  683,  691,  701,  709,  719,  727,  733,  739,  743,
    751,  757,  761,  769,  773,  787,  797,  809,  811,  821,  823,  827,
    829,  839,  853,  857,  859,  863,  877,  881,  883,  887,  907,  911,
    919,  929,  937,  941,  947,  953,  967,  971,  977,  983,  991,  997,
    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
    1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
    1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
    1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
    1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439,
    1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
    1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
    1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
    1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783,
    1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
    1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
    1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
    2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143,
    2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
    2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347,
    2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
    2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543,
    2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657,
    2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713,
    2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801,
    2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
    2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
    3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119,
    3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
    3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
    3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
    3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527,
    3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
    3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697,
    3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797,
    3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
    3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003,
    4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093,
    4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
    4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283,
    4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
    4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513,
    4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621,
    4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721,
    4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813,
    4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
    4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011,
    5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113,
    5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233,
    5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,
    5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
    5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
    5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653,
    5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743,
    5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849,
    5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
    5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073,
    6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173,
    6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271,
    6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359,
    6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
    6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581,
    6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
    6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803,
    6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907,
    6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
    7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121,
    7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229,
    7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349,
    7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487,
    7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
    7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669,
    7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757,
    7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
    7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009,
    8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,
    8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231,
    8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317,
    8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443,
    8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573,
    8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
    8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753,
    8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861,
    8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971,
    8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
    9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,
    9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311,
    9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413,
    9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491,
    9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623,
    9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
    9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829,
    9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929,
    9931, 9941, 9949, 9967, 9973};
int nfaca = 1229;

int gcd(int a, int b) {
  if ((0 == a) || (0 == b))
    return 0;
  a = abs(a);
  b = abs(b);
  if (a < b) {
    int tmp = a;
    a = b;
    b = tmp;
  }

  int r = a % b;
  while (r != 0) {
    a = b;
    b = r;
    r = a % b;
  }
  return b;
} // gcd

void prime_division(int n, int *fac, int *ex, int *nfac) {
  int q;
  *nfac = 0;
  n = abs(n);
  if (n == 1)
    return;
  q = int(sqrt(n));
  for (int i = 2; i <= q; i++)
    if (n % i == 0) {
      ex[*nfac] = 0;
      fac[*nfac] = i;
      do {
        ex[*nfac]++;
        n /= i;
      } while (n % i == 0);
      (*nfac)++;
    }
  if (n > 1) {
    fac[*nfac] = n;
    ex[*nfac] = 1;
    (*nfac)++;
  }
}

static inline long modf(long x, long f) { return x % f + (x < 0 ? f : 0); }

int main() {
  int n;
  cin >> n;
  forr(i, 0, n) cin >> a[n - i];
  int g = a[n];
  forr(i, 0, n - 1) if (a[i] != 0) g = gcd(g, a[i]);
  int facb[100];
  int exb[100];
  int nfacb;
  prime_division(g, facb, exb, &nfacb);
  unordered_map<int, bool> bh;
  forr(i, 0, nfacb - 1) bh[facb[i]] = true;

  if (a[0] != 0) {
    // int fac2[100];
    // int ex2[100];
    // int nfac2;
    prime_division(a[0], ps, exaa, &nfaca);
  }
  // cout << "nfaca " << nfaca << endl;

  forr(i, 0, nfaca - 1) {
    int f = ps[i];
    // cout << f << endl;
    /*bool found = false;
    forr(j,0,nfacb-1)
      if (f == facb[j]) {
        found = true;
        break;
      }
    if (found) continue;*/
    if (bh[f])
      continue;
    bool ok = true;
    if (f > 5000) {
      forr(r, 1, f - 1) {
        long v = a[0];
        long r2i = 1;
        forr(j, 1, n) {
          r2i = (r2i * r) % f;
          v = (v + a[j] * r2i) % f;
        }
        if (v != 0) {
          ok = false;
          break;
        }
      }

    } else {
      forr(j, 0, f - 2) c[j] = 0;
      forr(j, 0, n) c[j % (f - 1)] = (c[j % (f - 1)] + a[j]) % f;
      forr(r, 1, f - 1) {
        long v = c[0];
        long r2i = 1;
        forr(j, 1, f - 2) {
          r2i = (r2i * r) % f;
          v = (v + c[j] * r2i) % f;
        }
        if (v != 0) {
          ok = false;
          break;
        }
      }
    }
    if (ok)
      facb[nfacb++] = f;
  }
  vector<int> bb(nfacb);
  forr(i, 0, nfacb - 1) bb[i] = facb[i];
  sort(bb.begin(), bb.end());
  forr(i, 0, nfacb - 1) cout << bb[i] << endl;
}


Fixed submission:
// #include <bits/stdc++.h>
#include <algorithm> // min,max
#include <cmath>     // sqrt
#include <cstdlib>   // exit
#include <iostream>
#include <list>
#include <map>
#include <unordered_map>
#include <vector>
using namespace std;
#define forr(i, m, n) for (int i = (m); i <= (n); i++)
#define forv(i, m, n) for (int i = (m); i >= (n); i--)
#define forall(it, p) for (auto it = p.begin(); it != p.end(); ++it)
#define R 1000000007
#define DBG 1

#define MAXN 10002
int a[MAXN];
long c[MAXN];
int faca[MAXN];
int exaa[MAXN];
int ps[MAXN] = {
    2,    3,    5,    7,    11,   13,   17,   19,   23,   29,   31,   37,
    41,   43,   47,   53,   59,   61,   67,   71,   73,   79,   83,   89,
    97,   101,  103,  107,  109,  113,  127,  131,  137,  139,  149,  151,
    157,  163,  167,  173,  179,  181,  191,  193,  197,  199,  211,  223,
    227,  229,  233,  239,  241,  251,  257,  263,  269,  271,  277,  281,
    283,  293,  307,  311,  313,  317,  331,  337,  347,  349,  353,  359,
    367,  373,  379,  383,  389,  397,  401,  409,  419,  421,  431,  433,
    439,  443,  449,  457,  461,  463,  467,  479,  487,  491,  499,  503,
    509,  521,  523,  541,  547,  557,  563,  569,  571,  577,  587,  593,
    599,  601,  607,  613,  617,  619,  631,  641,  643,  647,  653,  659,
    661,  673,  677,  683,  691,  701,  709,  719,  727,  733,  739,  743,
    751,  757,  761,  769,  773,  787,  797,  809,  811,  821,  823,  827,
    829,  839,  853,  857,  859,  863,  877,  881,  883,  887,  907,  911,
    919,  929,  937,  941,  947,  953,  967,  971,  977,  983,  991,  997,
    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
    1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
    1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
    1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
    1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439,
    1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
    1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
    1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
    1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783,
    1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
    1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
    1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
    2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143,
    2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
    2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347,
    2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
    2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543,
    2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657,
    2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713,
    2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801,
    2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
    2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
    3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119,
    3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
    3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
    3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
    3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527,
    3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
    3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697,
    3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797,
    3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
    3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003,
    4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093,
    4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
    4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283,
    4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
    4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513,
    4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621,
    4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721,
    4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813,
    4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
    4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011,
    5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113,
    5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233,
    5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,
    5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
    5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
    5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653,
    5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743,
    5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849,
    5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
    5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073,
    6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173,
    6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271,
    6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359,
    6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
    6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581,
    6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
    6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803,
    6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907,
    6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
    7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121,
    7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229,
    7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349,
    7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487,
    7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
    7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669,
    7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757,
    7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
    7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009,
    8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111,
    8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231,
    8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317,
    8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443,
    8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573,
    8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
    8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753,
    8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861,
    8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971,
    8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
    9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199,
    9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311,
    9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413,
    9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491,
    9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623,
    9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
    9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829,
    9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929,
    9931, 9941, 9949, 9967, 9973};
int nfaca = 1229;

int gcd(int a, int b) {
  if ((0 == a) || (0 == b))
    return 0;
  a = abs(a);
  b = abs(b);
  if (a < b) {
    int tmp = a;
    a = b;
    b = tmp;
  }

  int r = a % b;
  while (r != 0) {
    a = b;
    b = r;
    r = a % b;
  }
  return b;
} // gcd

void prime_division(int n, int *fac, int *ex, int *nfac) {
  int q;
  *nfac = 0;
  n = abs(n);
  if (n == 1)
    return;
  q = int(sqrt(n));
  for (int i = 2; i <= q; i++)
    if (n % i == 0) {
      ex[*nfac] = 0;
      fac[*nfac] = i;
      do {
        ex[*nfac]++;
        n /= i;
      } while (n % i == 0);
      (*nfac)++;
    }
  if (n > 1) {
    fac[*nfac] = n;
    ex[*nfac] = 1;
    (*nfac)++;
  }
}

static inline long modf(long x, long f) { return x % f + (x < 0 ? f : 0); }

int main() {
  int n;
  cin >> n;
  forr(i, 0, n) cin >> a[n - i];
  int g = a[n];
  forr(i, 0, n - 1) if (a[i] != 0) g = gcd(g, a[i]);
  int facb[100];
  int exb[100];
  int nfacb;
  prime_division(g, facb, exb, &nfacb);
  unordered_map<int, bool> bh;
  forr(i, 0, nfacb - 1) bh[facb[i]] = true;

  if (a[0] != 0) {
    // int fac2[100];
    // int ex2[100];
    // int nfac2;
    prime_division(a[0], ps, exaa, &nfaca);
  }
  // cout << "nfaca " << nfaca << endl;

  forr(i, 0, nfaca - 1) {
    int f = ps[i];
    // cout << f << endl;
    /*bool found = false;
    forr(j,0,nfacb-1)
      if (f == facb[j]) {
        found = true;
        break;
      }
    if (found) continue;*/
    if (bh[f])
      continue;
    bool ok = true;
    if (f >= 10000) {
      forr(r, 1, f - 1) {
        long v = a[0];
        long r2i = 1;
        forr(j, 1, n) {
          r2i = (r2i * r) % f;
          v = (v + a[j] * r2i) % f;
        }
        if (v != 0) {
          ok = false;
          break;
        }
      }

    } else {
      forr(j, 0, f - 2) c[j] = 0;
      forr(j, 0, n) c[j % (f - 1)] = (c[j % (f - 1)] + a[j]) % f;
      forr(r, 1, f - 1) {
        long v = c[0];
        long r2i = 1;
        forr(j, 1, f - 2) {
          r2i = (r2i * r) % f;
          v = (v + c[j] * r2i) % f;
        }
        if (v != 0) {
          ok = false;
          break;
        }
      }
    }
    if (ok)
      facb[nfacb++] = f;
  }
  vector<int> bb(nfacb);
  forr(i, 0, nfacb - 1) bb[i] = facb[i];
  sort(bb.begin(), bb.end());
  forr(i, 0, nfacb - 1) cout << bb[i] << endl;
}