Scaled Dot-Product Attention by Hand

A single query attends to two key/value pairs using scaled dot-product attention,

$$\text{Attention}(q,K,V) = \text{softmax}\!\left(\frac{qK^\top}{\sqrt{d_k}}\right)V.$$

Take $q = [1, 0]$, keys $k_1 = [1, 0]$, $k_2 = [0, 1]$, values $v_1 = [1, 0]$, $v_2 = [0, 2]$ and $d_k = 2$.

The output is a 2-vector. Give its two components, first then second, as numbers separated by a comma (at least 4 significant figures).