Problem Statement

We have a sequence of N integers: $A_1, A_2, \cdots, A_N$.
You can perform the following operation between 0 and K times (inclusive):

• Choose two integers i and j such that $i \neq j$, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly producing a negative element.

Compute the maximum possible positive integer that divides every element of A after the operations. Here a positive integer x divides an integer y if and only if there exists an integer z such that y = xz.

Input

Input is given from Standard Input in the following format:
N K
$A_1 A_2 \cdots A_{N-1} A_{N}$

Output

Print the maximum possible positive integer that divides every element of A after the operations.

Constraints

• $2 \leq N \leq 500$
• $1 \leq A_i \leq 10^6$
• $0 \leq K \leq 10^9$
• All values in input are integers.

Sample Input 1

2 3
8 20

Sample Output 1

7

7 will divide every element of A if, for example, we perform the following operation:

• Choose i = 2, j = 1. A becomes (7, 21).

We cannot reach the situation where 8 or greater integer divides every element of A.

Sample Input 2

2 10
3 5

Sample Output 2

8

Consider performing the following five operations:

• Choose i = 2, j = 1. A becomes (2, 6).
• Choose i = 2, j = 1. A becomes (1, 7).
• Choose i = 2, j = 1. A becomes (0, 8).
• Choose i = 2, j = 1. A becomes (-1, 9).
• Choose i = 1, j = 2. A becomes (0, 8).

Then, $0 = 8 \times 0$ and $8 = 8 \times 1$, so 8 divides every element of A. We cannot reach the situation where 9 or greater integer divides every element of A.

Sample Input 3

4 5
10 1 2 22

Sample Output 3

7

Sample Input 4

8 7
1 7 5 6 8 2 6 5

Sample Output 4

5

见题面 Input 部分

见题面 Output 部分