You are given an integer array nums and a $\text{2D}$ integer array queries, where queries[i] $= [x_i, y_i]$.

For each query queries[i], calculate the sum of all elements nums[j] where $j = x_i + k \times y_i$ for all non negative integers $k$ such that $j <$ nums.length.

Return an array containing the answer for each query modulo $10^9 + 7$.

Constraints:

• n $==$ nums.length

• $1 \leq$ n $\leq 5 \times 10^4$

• $0 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ queries.length $\leq 1.5 \times 10^5$

• $0 \leq$ x_i $<$ n

• $1 \leq$ y_i $\leq 5 \times 10^4$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.