Assume that you have just built a dense b+ tree containing100,000 records, with one record per disk sector. the key field is a 20 byte string. pointers (i. e. record ids) are 4 byte values. the size of one disk sector is 1024 bytes. the index was built in a bottom-up fashion using the bulk-loading algorithm and that the nodes at each level were filled up as much as possible. a node corresponds to a disk sector.

a. how many key/pointer pairs fit within a b+ node?
b. how many levels does the resulting tree have?
c. how many leaf nodes are used by the tree?
d. how many total nodes (root, internal, leaf) are required?