資料結構與演算法

(4 points) 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

$h(k, i) = \big(h_1(k) + i\, h_2(k)\big) \bmod m.$

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 $k$)?