Equal Average

You are given a sequence $A_1, A_2, \ldots, A_N$ and an integer $K$. Determine if it is possible to reorder the elements of the sequence $A$ into a sequence $B_1, B_2, \ldots, B_N$ and choose a real number $m$ in such a way that for each contiguous subsequence of $B$ with length $K$, the arithmetic average of the elements of this subsequence is $m$. If it is possible, find one such reordered subse