Sum of Infinite Array Problem Statement

Given an array A of N integers, construct an infinite array B by repeating A indefinitely. Your task is to process Q queries, each defined by two integers L and R. For each query, calculate the sum of elements from index L to R (inclusive) in the infinite array B.

Return the sum modulo 10^9 + 7.

Example:

Input:

A = [1, 2, 3], Queries = [(1, 3), (2, 5)]

Output:

6 9

Explanation:

For the first query, the subarray from index 1 to 3 in B is [1, 2, 3], and the sum is 6. For the second query, the subarray from index 2 to 5 is [2, 3, 1, 2], and the sum is 9.

Constraints:

• 1 <= T <= 100
• 1 <= N <= 10^4
• 1 <= A[i] <= 10^9
• 1 <= Q <= 10^4
• 1 <= L <= R <= 10^18

Note:

You do not need to print anything; it has already been taken care of. Just implement the given function.