- Difficulty: Hard
- Tags: LeetCode, Hard, leetcode-3145, Binary Search, O(q * (logr)^2), O(1), Combinatorics, Bitmasks, Fast Exponentiation, Bit Manipulation, Array
Problem
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.
Example 1:
Input: queries = [[1,3,7]]
Output: [4]
Explanation:
There is one query.
big_nums[1..3] = [2,1,2]
. The product of them is 4. The remainder of 4 under 7 is 4.
Example 2:
Input: queries = [[2,5,3],[7,7,4]]
Output: [2,2]
Explanation:
There are two queries.
First 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.
Constraints:
1 <= queries.length <= 500
queries[i].length == 3
0 <= queries[i][0] <= queries[i][1] <= 1015
1 <= queries[i][2] <= 105