Now that we have the structure and a search algorithm, we also need to know how to insert new key/value pairs. The program must not attempt to insert the same key with both values. If the value is 0, insert the key into "A"0 and then test if the key is in "B"0. If so, this is a false positive for "B"0, and the key must also be inserted into "A"1 recursively in the same manner. If we reach the last level, we simply insert it. When the value is 1, the operation is similar but with "A" and "B" reversed.