You are given a 0-indexed integer array nums consisting of n non-negative integers.

You are also given an array queries, where queries[i] = [xi, yi]. The answer to the ith query is the sum of all nums[j] where xi <= j < n and (j - xi) is divisible by yi.

Return an array answer where answer.length == queries.length and answer[i] is the answer to the ith query modulo 109 + 7.

 

Example 1:

Input: nums = [0,1,2,3,4,5,6,7], queries = [[0,3],[5,1],[4,2]]
Output: [9,18,10]
Explanation: The answers of the queries are as follows:
1) The j indices that satisfy this query are 0, 3, and 6. nums[0] + nums[3] + nums[6] = 9
2) The j indices that satisfy this query are 5, 6, and 7. nums[5] + nums[6] + nums[7] = 18
3) The j indices that satisfy this query are 4 and 6. nums[4] + nums[6] = 10

Example 2:

Input: nums = [100,200,101,201,102,202,103,203], queries = [[0,7]]
Output: [303]

 

Constraints:

• n == nums.length
• 1 <= n <= 5 * 104
• 0 <= nums[i] <= 109
• 1 <= queries.length <= 1.5 * 105
• 0 <= xi < n
• 1 <= yi <= 5 * 104