Problem:
Score : 800 points

Problem Statement

You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x.

Constraints

0 \leq N \leq 10^4

|a_i| \leq 10^9(0\leq i\leq N)

a_N \neq 0

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_N
:
a_0

Output

Print all prime numbers p that divide f(x) for every integer x, in ascending order.

Sample Input 1

2
7
-7
14

Sample Output 1

2
7

2 and 7 divide, for example, f(1)=14 and f(2)=28.

Sample Input 2

3
1
4
1
5

Sample Output 2

There may be no integers that satisfy the condition.

Sample Input 3

0
998244353

Sample Output 3

998244353

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    long f(long[] A, long x)
    {
        long k = 1;
        long ret = 0;
        foreach (var item in A)
        {
            ret += item * k;
            k *= x;
        }
        return ret;
    }
    void solve()
    {
        int N = cin.nextint;
        var A = new long[N + 1];

        int odd = 0;
        for (int i = A.Length - 1; i >= 0; i--)
        {
            A[i] = cin.nextlong;
            if (i > 0 && Abs(A[i]) % 2 == 1)
            {
                odd++;
            }
        }

        var L = new List<long>();
        if (A[0] % 2 == 0 && odd % 2 == 0)
        {
            L.Add(2);
        }

        var G = gcd(f(A, 0), gcd(f(A, 1), f(A, -1)));

        //WriteLine(G);
        if (G % 2 == 0) G /= 2;
        
        for (long i = 3; i * i <= G; i++)
        {
            if (G % i == 0)
            {
                L.Add(i);
                var j = G / i;
                if (i != j) L.Add(j);
                G /= i;
            }
        }
        if (G != 1)
        {
            L.Add(G);
        }

        L.Sort();
        foreach (var item in L)
        {
            WriteLine(item);
        }
    }

    long gcd(long a, long b)
    {
        return (b != 0) ? gcd(b, a % b) : a;
    }
    long lcm(long a, long b)
    {
        return a / gcd(a, b) * b;
    }
    //ax + by = gcd(a, b)となるx, yを求める
    long extgcd(long a, long b, out long x, out long y)
    {
        long g = a;
        if (b != 0)
        {
            g = extgcd(b, a % b, out y, out x);
            y -= (a / b) * x;
        }
        else
        {
            x = 1;
            y = 0;
        }
        return g;
    }
}


static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}