for $1in-k.$ Observe that if $n=k,$ then any array of length $n$ is $k-$sorted, since there is only

one $k-$fold average in this case. We may also define any $A[1$cdotsn$]$ to be $k-$sorted if $kk[k]sort(A,1,n)kA[1$cdotsn$](k-1)n,$ since $in$

this case there are $nok-$fold averages. Modify Quicksort $to$ produce $an$ algorithm that $k-$sorts $an$

array $of$ any length. Write your algorithm $in$ pseudo$-$code and call $it$ Quick$[k]sort().$ Specifically,

the call Quick $[k]sort(A,1,n)$ will $k-$sort $A[1$cdotsn$],$ but will not necessarily $(k-1)-$sort the same

array. Prove the correctness $of$ your algorithm, and analyze its worst case run time.