A powerful array for an integer x is the shortest sorted array of powers of two that sum up to x. For example, the powerful array for 11 is [1, 2, 8].
The array big_nums is created by concatenating the powerful arrays for every positive integer i in ascending order: 1, 2, 3, and so forth. Thus, big_nums starts as [1, 2, 1, 2, 4, 1, 4, 2, 4, 1, 2, 4, 8, ...].
You are given a 2D integer matrix queries, where for queries[i] = [fromi, toi, modi] you should calculate (big_nums[fromi] * big_nums[fromi + 1] * ... * big_nums[toi]) % modi.
Return an integer array answer such that answer[i] is the answer to the ith query.
\n
Example 1:
\n\nInput: queries = [[1,3,7]]
\n\nOutput: [4]
\n\nExplanation:
\n\nThere is one query.
\n\nbig_nums[1..3] = [2,1,2]. The product of them is 4. The remainder of 4 under 7 is 4.
Example 2:
\n\nInput: queries = [[2,5,3],[7,7,4]]
\n\nOutput: [2,2]
\n\nExplanation:
\n\nThere are two queries.
\n\nFirst query: big_nums[2..5] = [1,2,4,1]. The product of them is 8. The remainder of 8 under 3 is 2.
Second query: big_nums[7] = 2. The remainder of 2 under 4 is 2.
\n
Constraints:
\n\n1 <= queries.length <= 500queries[i].length == 30 <= queries[i][0] <= queries[i][1] <= 10151 <= queries[i][2] <= 105f(n, i) which is the total number of numbers in [1, n] when the ith bit is set in O(log(n)) time.",
"Use binary search to find the last number for each query (and there might be one “incomplete” number for the query).",
"Use a similar way to find the product (we only need to save the sum of exponents of power of 2)."
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