SP6893 PWSUM - Power Sums

 Everyone knows that we can express sums of form sigma i = 1 to x ( i^k ) as polynomials

The first and only line of input contains a nonnegative integer k ( 0

The first and only line of output should contain the canonic coefficient representation of the formula. To elaborate, this should be the form of your output: a $ _{k+1} $ x $ ^{k+1} $ + a $ _{k} $ x $ ^{k} $ + a $ _{k-1} $ x $ ^{k-1} $ ... a $ _{0} $ x $ ^{0} $ ai here represents the coefficient that stands by the i-th power of x. As we only wish to find the formula modulo 10007, all the coefficients should be from interval \[0, 10006\] of integers. See the sample input and output for further clarification.