7478번 - Invariant Polynomials 다국어

문제

Consider a real polynomial P(x, y) in two variables. It is called invariant with respect to the rotation by an angle α if P(x cos α − y sin α, x sin α + y cos α) = P(x, y) for all real x and y. Let’s consider the real vector space formed by all polynomials in two variables of degree not greater than d invariant with respect to the rotation by 2π/n. Your task is to calculate the dimension of this vector space.

You might find useful the following remark: Any polynomial of degree not greater than d can be uniquely written in form $P(x, y)=\displaystyle\sum_{i,j\ge 0\atop i+j\le d} a_{ij} x^iy^j$ for some real coefficients a_ij.

입력

The input file contains two positive integers d and n separated by one space. It is guaranteed that they are less than one thousand.

출력

Output a single integer M which is the dimension of the vector space described.

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