SPOJ in Gyumri

   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 cosα  − y sinα , x sinα  + y cosα ) = 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

for some real coefficients a_ij .

Input

   The input file 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.

Examples