concept of maintaining number sets is not clear to me? Can you explain what help is it doing?

A number set means a set of numbers. We can choose some numbers (number set) from the origin array. Then our goal is make the XOR of these numbers choosen equals to K. But we can't do it directly. So we slowly maintain which number sets satisfy that after XOR, the first i bits equals to the first i bits of K.

corrct me if i am wrong. i think you are building the number set by bits and then if a particular bit int K is 0, and the current set contains number v1,v2,v3..vn then you are leaving numbers containing bitk( k'th bit 0) unchanged while those numbers having kth bit 1 you are combining them even numbers at a time like v1 XOR v2, v2 XOR v3 ... and probably removing the v1,v2.. . BUT how it takes care of cases like v1 XOR v2 XOR v3 XOR v4

For v1 XOR v2 XOR v3 XOR v4
You can choose (v1 XOR v2) and (v3 XOR v4)
Both ((v1 XOR v2) and (v3 XOR v4)) are (s')'s elements.
We use a set of numbers, s, to represent a exponential number of number sets.
We can restore these 2^N number sets by either to choose and not to choose each element in s.
For example, if s={1,2,3}, it represent the following number sets:
{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}
So, s is not the 2^N number sets itself, we just try to represent and store it in this way.

BTW, would you mind if I copy our Q&A as comments on my blog, code scenic?
I think these would help others understand what I mean.

not at all.

Thanks!
And could you understand it now? :)

still on way.