Recently I come acroos a tecnique similar to Polyci based DS, a Policy Based Persistent BIT. To basic idea is to keep the BIT balanced by HLD. Naive algo is O(n^2). But you have to optimise using bitset to make it O(nlog n). You can perform dynamic range update range query and orthogonal range minimum IDA* search easily in O(Nlog N).
This can be solved with this trick easily combining this with Baby Step Giant Sweep line. Along with persistent 3SAT.