How to split binomial heap in O(log(n))?

Hello.

The question is how to split binomial heap (size n) into binomial heap
of size k (k<n) and binomial heap of size n-k within O(log(n))
complexity .

I've thought of something like traveling through binomial trees list
( from zero to higher orders ) until sum of the trees' sizes exceeds
k , stepping back , breaking the next tree unto chunks and joining
the chunks with smaller trees until I'd get k elements.

But this seems too complicated and messy to implement and it would
surely take more then log(n) because of joining .

Is over there some simple algorithm that does the job in given
O(log(n)) complexity ?

Thanks in advance,

.