--description--

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

$$\begin{align} S_0 & = 290\,797 \\ S_{n + 1} & = {S_n}^2\bmod 50\,515\,093 \end{align}$$

Let $A(i, j)$ be the minimum of the numbers $S_i, S_{i + 1}, \ldots, S_j$ for $i ≤ j$. Let $M(N) = \sum A(i, j)$ for $1 ≤ i ≤ j ≤ N$.

We can verify that $M(10) = 432\,256\,955$ and $M(10\,000) = 3\,264\,567\,774\,119$.

Find $M(2\,000\,000\,000)$.

--hints--

minimumOfSubsequences() should return 7435327983715286000.

assert.strictEqual(minimumOfSubsequences(), 7435327983715286000);

--seed--

--seed-contents--

function minimumOfSubsequences() {

  return true;
}

minimumOfSubsequences();

--solutions--

// solution required