There is a array of length A. We have to perform B operations. In each operation, we can select a subarray of any length and increase all its elements by 1. All subarrays are equiprobable. Find the expected value of the square of the sum of elements. (mod 1e9+7)
Constraints:
1<=A,B<=1e9
Sample Input 1:
A=2
B=2
There are 9 different order of operations.
(0,0) + (1,1) = 2
(0,0) + (0,0) = 2
(1,1) + (0,0) = 2
(1,1) + (1,1) = 2
(0,1) + (0,0) = 3
(0,1) + (1,1) = 3
(0,0) + (0,1) = 3
(1,1) + (0,1) = 3
(0,1) + (0,1) = 4
Expected Value= [4*(2^2) + 4*(3^2) + (4^2)]/9 = 68/9 (mod 1e9+7) = 555555567
How do I approach this problem?
