Consider a four$-$level B$-$tree; that is$,$ there is one leaf level and three nonleaf levels. When we talk about leaf nodes, we do not include the sequence pointer $($pointer to next leaf to the right$).$ Assume that nodes have slots for $100$ keys. Calculate the maximum and minimum numbers of pointers and keys at the root, the leaves, and at interior nodes other than the root. What are the minimum and maximum number of records that are indexed by this B$-$tree? Which of the following statements is true?$$

$$a$)$The maximum number of pointers for a nonleaf, nonroot node is $100.$b$)$The minimum number of pointers for a leaf, nonroot node is $51.$c$)$The minimum number of pointers for a nonleaf, nonroot node is $50.$d$)$The maximum number of pointers for a leaf, nonroot node is $100.$