Oneness

Define the oneness of a number $x$ as the number of integers $d > 1$ that divide $x$ and whose decimal representation consists only of the digit $1$. For example, $oneness(121) = 1$ and $oneness(1221) = 2$.

The number $n$ is generated by a pseudo-random number generator. You are given two integers $l$ and $s_0$, where $l$ is the number of digits in the decimal representation of $n$ and $s_0$ is the seed of the generator. The digits $d_0 d_1 \ldots d_{l-1}$ of $n$ are generated by the following recurrences:

$d_i = \left\lfloor s_i / 1024 \right\rfloor \mod 10$

$s_{i+1} = (747796405 s_i - 1403630843) \mod 2^{32}$

It is guaranteed that $d_0$ is non-zero. Calculate the total oneness over all integers between $1$ and $n$.

The first line contains two integers $l$ and $s_0$ ($1 \le l \le 250\,000$, $0 \le s_0 < 2^{32}$).

Output the sum of the oneness over all integers between $1$ and $n$.

In the sample tests, $n$ equals 1, 11, 1221, and 9359, respectively.