Problem 375: Minimum of subsequences

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

S0

=

290797

Sn+1

=

Sn2 mod 50515093

Let A(i, j) be the minimum of the numbers Si, Si+1, ... , Sj 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).