You are given an integer array nums of size n. For each index i where 0 <= i < n, define a subarray nums[start ... i] where start = max(0, i - nums[i]).

Return the total sum of all elements from the subarray defined for each index in the array.

 

Example 1:

Input: nums = [2,3,1]

Output: 11

Explanation:

i Subarray Sum
0 nums[0] = [2] 2
1 nums[0 ... 1] = [2, 3] 5
2 nums[1 ... 2] = [3, 1] 4
Total Sum   11

The total sum is 11. Hence, 11 is the output.

Example 2:

Input: nums = [3,1,1,2]

Output: 13

Explanation:

i Subarray Sum
0 nums[0] = [3] 3
1 nums[0 ... 1] = [3, 1] 4
2 nums[1 ... 2] = [1, 1] 2
3 nums[1 ... 3] = [1, 1, 2] 4
Total Sum   13

The total sum is 13. Hence, 13 is the output.

 

Constraints: