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) = Σ_{i,j>=0,i+j<=d}a_ijxⁱy^j

for some real coefficients a_ij

.

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