A note about claw function with a small range

In the claw detection problem we are given two functions $f:Drightarrow R$ and $g:Drightarrow R$ ($|D|=n$, $|R|=k$), and we have to determine if there is exist $x,yin D$ such that $f(x)=g(y)$. We show that the quantum query complexity of this problem is between $Omegaleft(n^{1/2}k^{1/6}right)$ and $Oleft(n^{1/2+varepsilon}k^{1/4}right)$ when $2leq k<n$.