Suppose that we use double hashing to resolve collisions—that is, we use the hash function h(k, i) = (h₁(k) + ih₂(k)) mod m. Show that if m and h₂(k) have greatest common divisor d ≥ 1 for some key k, then an unsuccessful search for key k examines (1/d)th of the hash table before returning to slot h₁(k). Thus, when d = 1, so that m and h₂(k) are relatively prime, the search may examine the entire hash table.