Given a finite sequence {x1,x2,...,xN}, shifting the sequence gives the sequence {x2,x3,...,xN,x1}. Prove that for any sequence of N real numbers, if the sum of the numbers is non-negative, then one can shift the sequence some number of times so that the resulting sequence has the following property: for each K <= N, the sum of the first K numbers in the resulting sequence is non-negative.