Flatten Nested Map into List with Depth-First Search Ordering

In clojure, how can I turn a nested map like this:

{"1" {"1.1" {"1.1.1" {}
             "1.1.2" {}}
      "1.2" {}}
 "2" {"2.1" {}
      "2.2" {}
      "2.3" {}}}

Into this:

("1" "1.1" "1.1.1" "1.1.2" "1.2" "2" "2.1" "2.2" "2.3")

Here is a straightforward iterative solution (using loop and recur):

(defn flatten-map [m]
  (loop [in m out []]
    (if-let [[[k v] & ts] (seq in)]
      (recur (concat v ts)
             (conj out k))
      out)))

And a "fancy" one (using tree-seq function)

(defn flatten-map [m]
  (->> [nil m]
       (tree-seq sequential? second)
       (drop 1)
       (map first)))