Alan has an ~N~ by ~M~ array of integers ~a_{ij}~. Alan knows that he can make rectangles in the array and sum the elements contained in the rectangle, and calls it a "rectangle-sum". He wondered about sum of all rectangle-sums for all possible rectangles, but because Alan is too good at math, he already figured out the answer. Instead, he asks you to find the sum of all rectangle-sums for all rectangles where both dimensions are less than or equal to ~K~ (the length/width of a rectangle is how many elements it spans). Because this number can be very large, Alan asks for it modulo ~10^9+7~. Can you help Alan?

Input Specification

The first line will contain 3 integers ~N, M, K\ (1 \le N, M, K \le 10^9)~.

Output Specification

Output the answer to Alan's question, modulo ~10^9+7~.

Subtasks

Subtask 1 [20%]

~0 < a_{ij} \le 1 \le N, M, K \le 1000~

Subtask 2 [30%]

~0 < a_{ij} \le 1 \le N, M, K \le 10^6~

Subtask 3 [50%]

~0 < a_{ij} \le 1~

Sample Input

3 3 2

Sample Output

49