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. 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 i^th query. Since the answer to the i^th 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]For
n = 15, powers = [1, 2, 4, 8], so the query products are 1 * 2 = 2, 4, and 1 * 2 * 4 * 8 = 64.Example 2
Input
n = 2, queries = [[0,0]]Output
[2]For
n = 2, powers = [2], so the only query returns 2.Constraints
- 1 <= n <= 10^9
- 1 <= queries.length <= 10^5
- 0 <= starti <= endi < powers.length