405016: GYM101741 F GCD

You are given an array of integers a₁, a₂, ..., a_n.

Find the maximum possible greatest common divisor of all numbers from the array if you can erase no more than k elements () 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 ≤ n ≤ 10⁵, ).

The second line contains n integers a₁, a₂, ..., a_n: the array a (1 ≤ a_i ≤ 10¹⁸).

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

4 1
6 15 35 14

1

4 2
6 15 35 14

7

3 1
897612484786617600 5828 16027

1457