TopCoder problem "MegaSum" used in SRM 454 (Division I Level Three)

Problem Statement
	Let us define an infinite table of integers as follows: Each cell is uniquely identified by the value it contains. Let us define S(X) as the sum of all the values in the rectangle with cell 1 as its upper-left corner and cell X as its lower-right corner. For example, S(12) is the sum of all the values in the green rectangle shown above. You are given a long N. First, find the rectangle with cell 1 as its upper-left corner and cell N as its lower-right corner. Then, calculate the sum of S(X) for all values X inside this rectangle. Return this sum modulo 1,000,000,007. For example, if N is 8, you would first find the 3 x 2 rectangle with 1 in its upper-left corner and 8 in its lower-right corner. You would then calculate S(X) for each value X in this rectangle: S(1) = 1, S(2) = 3, S(9) = 12, S(4) = 5, S(3) = 10, and S(8) = 27. You would them sum these values to get 1 + 3 + 12 + 5 + 10 + 27 = 58.
Definition
	Class: MegaSum Method: calculate Parameters: long Returns: int Method signature: int calculate(long N) (be sure your method is public)
Constraints
-	N will be between 1 and 10^10, inclusive.
Examples
0)
	8 Returns: 58 This is the example from the problem statement.
1)
	12 Returns: 282
2)
	11 Returns: 128
3)
	6 Returns: 50
4)
	34539 Returns: 437909839

Problem url:

Problem stats url:

Writer:

Testers:

Problem categories: