#### Recently I found one amazing problem on Hackerearth that seems to be difficult to be solved within time limits.

we are given an array A of n positive integers and we are supposed to calculate **MGCD**(k) of A. Here **MGCD**(k) is the Modified GCD of Order K for an Array A.

Modified GCD of Order K for an array is the Maximum number that divides at least **ceil**(n/k) number of elements of the array.For example Modified Gcd of Order 2 for array A is the Maximum number that divides at least half of its elements. For example-given n=10, k=3 and array A={24 18 28 8 25 1 48 27 56 16}

In the above example 8 divides 5 elements of the array(24,8,48,56,16) ,which is greater than(>=) **ceil**(10/3) i.e.=4 There is no number greater 8 than that divides at least 4 numbers of the array.So 8 is the required answer.