Name Reduction

In an attempt to reduce the growing population, Archer was asked to come up with a plan. Archer being as intelligent as he is, came up with the following plan: If $N$ children, with names $C_{1}, C_{2}, ... , C_{N}$, are born to parents with names $A$ and $B$, and you consider $C$ to be the concatenation of all the names of the children, i.e. $C = C_{1} + C_{2} + ... + C_{N}$ (where $+$ is concat