Polynomial Divisors

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.

Examples

Input

2 7 -7 14

Output

2 7

Input

3 1 4 1 5

Output

Input

0 998244353

Output

998244353

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N a_N : a_0

outputFormat

Output

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

Examples

Input

2 7 -7 14

Output

2 7

Input

3 1 4 1 5

Output

Input

0 998244353

Output

998244353

样例

2
7
-7
14

2
7

</p>