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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"

using namespace std;

//const long long int MOD = 1000000007;
//const int MOD = 1000000007;
const int MOD = 998244353;
//const long long int MOD = 998244353;

long long int N, M, K, H, W, L, R;
//int N, M, K, H, W, L, R;

list<int> Prime(int num) {
	list<int>P;
	for (int i = 5; i <= num; i += 6) {
		bool flag = true;
		for (auto j : P) {
			if (j*j > i) {
				break;
			}
			if (i%j == 0) {
				flag = false;
				break;
			}
		}
		if (flag)P.push_back(i);
		flag = true;
		for (auto j : P) {
			if (j*j > i + 2) {
				break;
			}
			if ((i + 2) % j == 0) {
				flag = false;
				break;
			}
		}
		if (flag)P.push_back(i + 2);
	}
	P.push_front(3);
	P.push_front(2);
	return P;
}

int gcd(int a, int b) {
	while (b) {
		a %= b;
		swap(a, b);
	}
	return a;
}


int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	cin >> N;
	vector<int>v(N + 1);
	for (auto &i : v)cin >> i;
	auto P = Prime(sqrt(10000000000000));
	vector<long long int>ans;
	long long int box = abs(accumulate(v.begin(), v.end(), 0LL));
	assert(box);
	for (auto i : P) {
		if (box%i)continue;
		ans.push_back(i);
		while (box%i == 0)box /= i;
	}
	if (box > 1)ans.push_back(box);
	vector<long long int>ret;
	for (auto j : ans) {
		if (v.back() % j == 0)ret.push_back(j);
	}
	for (auto i : ret)cout << i << endl;
	return 0;
}