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[i] = [lefti, righti]. Each
queries[i] represents a query where you have to find the product of all
lefti <= j <= righti.
Return an array
answers, equal in length to
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
109 + 7.
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 * powers = 1 * 2 = 2. Answer to 2nd query: powers = 4. Answer to 3rd query: powers * powers * powers * powers = 1 * 2 * 4 * 8 = 64. Each answer modulo 109 + 7 yields the same answer, so [2,4,64] is returned.
Input: n = 2, queries = [[0,0]] Output:  Explanation: For n = 2, powers = . The answer to the only query is powers = 2. The answer modulo 109 + 7 is the same, so  is returned.
1 <= n <= 109
1 <= queries.length <= 105
0 <= starti <= endi < powers.length