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문제

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.

입력

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 $a$ ($1 \le a_i \le 10^{18}$).

출력

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

예제 입력 1

4 1
6 15 35 14

예제 출력 1

1

예제 입력 2

4 2
6 15 35 14

예제 출력 2

7

예제 입력 3

3 1
897612484786617600 5828 16027

예제 출력 3

1457