19329번 - GCD 다국어

You are given an array of integers $a_1, a_2, \ldots, a_n$.

Find the maximum possible greatest common divisor of all numbers from the array if you can erase no more than $k$ elements ($k \le \frac{n}{2}$) from this array.

The first line contains two integers: $n$, the number of elements in the array, and $k$, the maximum number of elements you can erase ($2 \le n \le 10^5$, $0 \le k \le \frac{n}{2}$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$: the array $a$ ($1 \le a_i \le 10^{18}$).

Print the maximum possible greatest common divisor of all elements of the array after erasing no more than $k$ elements.