Range Product Queries of Powers

Decompose integer n into its set-bit powers of two, then answer range queries asking for the product of powers within [l, r]. Use a prefix-product array modulo 10^9 + 7 for O(1) per query.

Examples
Input: [15,[[0,1],[2,2],[0,3]]]
Output: [2,4,64]
Hints

Range Product Queries of Powers

Decompose integer `n` into its set-bit powers of two, then answer range queries asking for the product of powers within `[l, r]`. Use a prefix-product array modulo `10^9 + 7` for O(1) per query.