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Language: 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 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 _{i,j>=0,i+j<=d}a_{ij}x^{i}y^{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. Sample Input 2 2 Sample Output 4 Source Northeastern Europe 2003, Northern Subregion |

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