## Minimum of subsequences

### Problem 375

Published on Saturday, 10th March 2012, 10:00 pm; Solved by 494; Difficulty rating: 40%Let `S`_{n} be an integer sequence produced with the following pseudo-random number generator:

S_{0} |
=_{ } |
290797_{ } |

S_{n+1} |
=_{ } |
S_{n}^{2} mod 50515093 |

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).