Let S_n be an integer sequence produced with the following pseudo-random number generator:

Let A(i, j) be the minimum of the numbers S_i, S_i+1, ... , S_j for i ≤ j.
Let M(N) = ΣA(i, j) for 1 ≤ i ≤ j ≤ N.
We can verify that M(10) = 432256955 and M(10 000) = 3264567774119.

Find M(2 000 000 000).