  We present a differentially private algorithm for releasing the sequence of
$k$ elements with the highest counts from a data domain of $d$ elements. The
algorithm is a "joint" instance of the exponential mechanism, and its output
space consists of all $O(d^k)$ length-$k$ sequences. Our main contribution is a
method to sample this exponential mechanism in time $O(dk\log(k) + d\log(d))$
and space $O(dk)$. Experiments show that this approach outperforms existing
pure differential privacy methods and improves upon even approximate
differential privacy methods for moderate $k$.
