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 $y = xz$.

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.

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.