3145 - Find Products of Elements of Big Array.

Hard

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 <code><ins>1</ins>, <ins>2</ins>, <ins>1, 2</ins>, <ins>4</ins>, <ins>1, 4</ins>, <ins>2, 4</ins>, <ins>1, 2, 4</ins>, <ins>8</ins>, ...</code>.

You are given a 2D integer matrix queries, where for <code>queriesi = from_i, to_i, mod_i</code> you should calculate <code>(big_numsfrom_i * big_numsfrom_i + 1 * ... * big_numsto_i) % mod_i</code>.

Return an integer array answer such that answer[i] is the answer to the <code>i^th</code> 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

• <code>0 <= queries0<= queries1<= 10¹⁵</code>

• <code>1 <= queries2<= 10⁵</code>