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Construct a $B^+$-tree for the following set of key values:
$(2, 3, 5, 7, 11, 17, 19, 23, 29, 31)$
Assume that the tree is initially empty and values are added in ascending order. Construct B+-trees for the cases where the number of pointers that will fit in one node is as follows:
a. Four
b. Six
c. Eight
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