#P2129. Invariant Polynomials

    ID: 1139 远端评测题 2000ms 64MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>Northeastern Europe 2003, Northern Subregion

Invariant Polynomials

Description

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) = Σi,j>=0,i+j<=daijxiyj

for some real coefficients aij .

Input

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

Output

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

2 2
4

Source

Northeastern Europe 2003, Northern Subregion