Using sequences of reduction functions changes how lookup is done: because the hash value of interest may be found at any location in the chain, it's necessary to generate "k" different chains. The first chain assumes the hash value is in the last hash position and just applies R"k"; the next chain assumes the hash value is in the second-to-last hash position and applies R"k"−1, then H, then R"k"; and so on until the last chain, which applies all the reduction functions, alternating with H. This creates a new way of producing a false alarm: if we "guess" the position of the hash value wrong, we may needlessly evaluate a chain.