Problem Statement

Given is a sequence of N positive integers: $A = (A_1, A_2, \ldots, A_N).$ You can do the following operation on this sequence at least zero and at most K times:

• choose $i\in$ ${1,2,\ldots,N$} and add 1 to A_i.

Find the maximum possible value of $\gcd(A_1, A_2, \ldots, A_N)$ after your operations.

Input

Input is given from Standard Input in the following format:
N K
$A_1 A_2 \ldots A_N$

Output

Print the maximum possible value of $\gcd(A_1, A_2, \ldots, A_N)$ after your operations.

Constraints

• $2\leq N\leq 3\times 10^5$
• $1\leq K\leq 10^{18}$
• $1 \leq A_i\leq 3\times 10^5$

Sample Input 1

3 6
3 4 9

Sample Output 1

5

One way to achieve $\gcd(A_1, A_2, A_3) = 5$ is as follows.

• Do the operation with i = 1 twice, with i = 2 once, and with i = 3 once, for a total of four times, which is not more than K=6.
• Now we have A_1 = 5, A_2 = 5, A_3 = 10, for which $\gcd(A_1, A_2, A_3) = 5$.

Sample Input 2

3 4
30 10 20

Sample Output 2

10

Doing no operation achieves $\gcd(A_1, A_2, A_3) = 10$.

Sample Input 3

5 12345
1 2 3 4 5

Sample Output 3

2472

见题面 Input 部分

见题面 Output 部分