Editorial for COCI '14 Contest 1 #1 Prosjek

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Let $S_k$ ~S_k~ be the sum of the first $k$ ~k~ numbers in sequence $A$ ~A~. It holds:

$\displaystyle B_k = \frac{S_k}{k}$ $$\displaystyle B_k = \frac{S_k}{k}$$

It follows:

$\displaystyle B_{k+1} = \frac{S_k+A_{k+1}}{k+1}$

From here we get the expression for $A_{k+1}$ ~A_{k+1}~:

$\displaystyle A_{k+1} = (k+1)B_{k+1}-S_k$

We calculate elements of the sequence $A_{k+1}$ ~A_{k+1}~ and their sum $S_k$ ~S_k~ iteratively by using one loop over sequence $B$ ~B~.

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