I would like to explain the Gaussian Elimination method which I have used and got AC in 0.00 
The link to my solution. (sorry for some dubugging statements in it).
- The idea here is to choose a no.
which has MSB with maximum value.
With a little thinking, we will get
the max(array) will have this
feature. Say, maximum of array is a
k-bit no. and that no. is M. Now,
there can be multiple no.s which are
k-bit no.s and have the same
highest-value bit as ‘1’. So in that
case we will EX-OR each of them with
the M and put them again input array
(ideally, we can choose any one of
those k-bit no.s as M and put others
in array after ex-oring with it). At
the same time we will keep the no. M
in some other array say x[]. - We will keep doing step 1 until we
get 0 as maximum in the array i.e.
this loop will run for iterations =
no. of bit the maximum of array is. - Now will have a x[] array which will
be of size = no. of bit the maximum
of array is - Now we will initialize the answer
variable to given K (because we want
it compulsorily) and loop for each
value in array x[], if value of
answer variable is going to increase
with the inclusion of ith element,
we will update the answer variable
with the new value as answer^x[i],
else we will keep it as is. - Finally returning the value of
answer solves our problem.
About my solution:
Bucket[i] contains all i-bit no.s
the M chosen is first element of bucket i.e. Bucket[i][0]
x[] is modified_array[]