Sums of Two

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:

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

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 $$$a + b = s$$$.

Input

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

Output

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

Example

Input

4 179629

Output

Note

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