Chef and Hills

Chefland is a $1D$ city where each of the $N$ houses is located at a distinct **positive integer** coordinate $A_1, A_2, \ldots A_N$. The chef is planning to create $K$ hills in the city. Note that two hills cannot be present at the same location but the location of hills and houses can overlap and each hill will also be at any **integer (positive, negative or zero)** coordinate. Each citizen