Minimum Operations to Make Array Elements Zero

For each query [l,r], you must reduce every integer in nums = [l..r] to zero by repeatedly picking two elements and replacing them with floor(a/4) and floor(b/4), and return the sum of the minimal number of such pair-operations across all queries. The core challenge is to compute, for large ranges (l,r up to 1e9 and up to 1e5 queries), how many division-by-4 steps each value needs and how to optimally pair levels of reductions (a counting/greedy formula) rather than simulating.