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Sum of powers
A young schoolboy would like to calculate the sum
for some fixed natural k and different natural n. He observed that calculating ik for all i (1<=i<=n) and summing up results is a too slow way to do it, because the number of required arithmetical operations increases as n increases. Fortunately, there is another method which takes only a constant number of operations regardless of n. It is possible to show that the sum Sk(n) is equal to some polynomial of degree k+1 in the variable n with rational coefficients, i.e.,
We require that integer M be positive and as small as possible. Under this condition the entire set of such numbers (i.e. M, ak+1, ak, ... , a1, a0) will be unique for the given k. You have to write a program to find such set of coefficients to help the schoolboy make his calculations quicker.
The input file contains a single integer k (1<=k<=20).
Write integer numbers M, ak+1, ak, ... , a1, a0 to the output file in the given order. Numbers should be separated by one space. Remember that you should write the answer with the smallest positive M possible.
6 2 3 1 0
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