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: