Design an implementation of the following operations in a binomial heap, assuming that all operations get a pointer to element x:

BHDecreaseKey$($H$,$ x$,$ k$),$ which reduces the value of element x to k; BHIncreaseKey$($H$,$ x$,$ k$),$ which increases the value of element x to k;

BHDelete$($H$,$x$),$ which removes the element x from the heap H$.$