Range Product Queries of Powers
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.
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 queries[i] = [lefti, righti]. Each queries[i] represents a query where you have to find the product of all powers[j] with lefti <= j <= righti.
Return an array answers, equal in length to queries, where answers[i] is the answer to the ith query. Since the answer to the ith query may be too large, each answers[i] should be returned modulo 10^9 + 7.
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: powers[0] * powers[1] = 1 * 2 = 2. Answer to 2nd query: powers[2] = 4. Answer to 3rd query: powers[0] * powers[1] * powers[2] * powers[3] = 1 * 2 * 4 * 8 = 64. Each answer modulo 10^9 + 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 powers[0] = 2. The answer modulo 10^9 + 7 is the same, so [2] is returned.
Constraints
- 1 <= n <= 10^9
- 1 <= queries.length <= 10^5
- 0 <= starti <= endi < powers.length
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