2438 - Range Product Queries of Powers\.

Medium

Given a positive integer n, there exists a 0-indexed array called powers, composed of the minimum number of powers of 2 that sum to n. The array is sorted in non-decreasing order, and there is only one way to form the array.

You are also given a 0-indexed 2D integer array queries, where <code>queriesi = left_i, right_i</code>. Each queries[i] represents a query where you have to find the product of all powers[j] with <code>left_i<= j <= right_i</code>.

Return an array answers, equal in length to queries, where answers[i] is the answer to the <code>i^th</code> query. Since the answer to the <code>i^th</code> query may be too large, each answers[i] should be returned modulo <code>10⁹ + 7</code>.

Example 1:

Input: n = 15, queries = \[\[0,1],2,2,0,3]

Output: 2,4,64

Explanation:

For n = 15, powers = 1,2,4,8. It can be shown that powers cannot be a smaller size.

Answer to 1st query: powers0 * powers1 = 1 * 2 = 2.

Answer to 2nd query: powers2 = 4.

Answer to 3rd query: powers0 * powers1 * powers2 * powers3 = 1 * 2 * 4 * 8 = 64.

Each answer modulo 10⁹ + 7 yields the same answer, so 2,4,64 is returned.

Example 2:

Input: n = 2, queries = \[\[0,0]]

Output: 2

Explanation: For n = 2, powers = 2. The answer to the only query is powers0 = 2. The answer modulo 10⁹ + 7 is the same, so 2 is returned.

Constraints:

• <code>1 <= n <= 10⁹</code>

• <code>1 <= queries.length <= 10⁵</code>

• <code>0 <= start_i<= end_i< powers.length</code>