Circular Permutation Recovery

You are given two integers $N, K$ such that $K + 1 \le N \le 2K-1$. Your friend is hiding from you a permutation $(P_1, P_2, \ldots, P_N)$ of integers from $1$ to $N$, whose elements are written cyclically. Your friend doesn't tell you the permutation. Instead, he tells you this. For each $i$ from $1$ to $N$ he will tell you $A_i$ $-$ the number of such integers $j$ with $0 \le j < K$ such that $