Assume that there are $K$ possible keys $\{1,2,\dots,K\}$ and $m$ hash table slots $\{0,1,\dots,m-1\}$ with $m>1$. In double hashing, the probe sequence is $h(k,i) = (h_1(k) + i \cdot h_2(k)) \mod m$. For a fixed key $k$, we want the sequence $h(k,0), h(k,1), \dots$ to visit all $m$ table slots before repeating, so that insertion succeeds whenever the table is not full. Which of the following conditions is necessary and sufficient for this property (for that key $k$)?