Given a positive integer n, consider an array powers consisting of the minimum number of powers of $2$ that sum up to n, sorted in ascending order.

You are also given a $2$D integer array queries, where each queries[i] = [start_i, end_i]. For each query, compute the product of all elements from powers[start_i] through powers[end_i] inclusive.

Return an array where each element is the result of the corresponding query.

Note: Since the results may be large, return each answer modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 10^9$

• $1 \leq$ queries.length $\leq 10^5$

• $0 \leq$ start_i $\leq$ end_i $<$ powers.length

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.