\begin{problem}{Sums of Two}{\textsl{standard input}}{\textsl{standard output}}{2 seconds}{1024 mebibytes}

Lina the Magician claims that a common modern computer
can easily perform a hundred billion operations per second!
To prove it, she proposes to run the following calculations.

Let $V$ be a set of integers, initially empty.
We are given the starting value of the integer $s$.
Make $n$ steps described below:

\begin{itemize}
\item $s \leftarrow (s \cdot 618\,023 + 1) \bmod 999\,983$;
\item find the number of distinct pairs of integers in $V$
that have the sum $s$;
\item if this number is even, insert $s$ into the set $V$.
\end{itemize}

How many elements will there be in $V$ after $n$ steps?

Formally: on each step, we count the number of pairs $(a, b)$
where $a \in V$, $b \in V$, $a \le b$ and $a + b = s$.


\InputFile
The first line contains integers $n$ and $s$
($1 \le n \le 200\,000$; $0 \le s < 999\,983$; $s \ne 742\,681$).


\OutputFile
Print a single integer: the size of set $V$ after $n$ steps.


\Example

\begin{example}
\exmpfile{example.01}{example.01.a}%
\end{example}

\Note
In the example, the values of $s$ on the four steps are
$740\,740$, $139\,655$, $469\,353$, and~$880\,395$.


\end{problem}

