Before revision:  We develop a data structure with O( n log log n ) space,  O( log n + k ) query time, and expected O( n polylog n ) preprocessing time , removing a ( log^2 n log log n ) -factor from the O( n ( log^2 n )( log log n )^2 ) space of Bohler et al 's recent SoCG'16 work. In addition, our dynamic version (that allows insertions and deletions of sites) also improves the space of Kaplan et al.'s recent SODA'17 work from O( n log^3 n ) to O( n log n ) , and reduces a ( log^2 n )-factor from their deletion time.
After revision:  We develop a data structure with O( n log log n ) space, O( log n + k ) query time, and expected O( n polylog n ) preprocessing time , removing a ( log^2 n log log n ) -factor from the O( n ( log^2 n )( log log n )^2 ) space of Bohler et al .'s work. Our dynamic version (that allows insertions and deletions of sites) also improves the space of Kaplan et al.'s recent SODA'17 work from O( n log^3 n ) to O( n log n ) , and reduces a ( log^2 n )-factor from their deletion time.