Invariant Polynomials

Consider a real polynomial $P(x, y)$ in two variables. We call it invariant under the rotation by an angle $\alpha$ if

$P(x\cos\alpha - y\sin\alpha,\; x\sin\alpha + y\cos\alpha) = P(x, y)$

holds for all real $x$ and $y$.

Consider the real vector space of all two-variable polynomials of degree at most $d$ that are invariant under the rotation by $2\pi/n$. Compute the dimension $M$ of this vector space.

You may find the following remark useful: every polynomial of degree at most $d$ can be written uniquely as

$P(x, y) = \sum_{\substack{i, j \ge 0 \\ i + j \le d}} a_{ij}\, x^i y^j$

for some real coefficients $a_{ij}$.

A single line with two positive integers $d$ and $n$ separated by one space. Both are less than $1000$.

Output a single integer $M$, the dimension of the vector space described above.