F. GCD
time limit per test
4 seconds
memory limit per test
512 mebibytes
input
standard input
output
standard output

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

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.

Input

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, ..., an: the array a (1 ≤ ai ≤ 1018).

Output

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

Examples
Input
4 1
6 15 35 14
Output
1
Input
4 2
6 15 35 14
Output
7
Input
3 1
897612484786617600 5828 16027
Output
1457