SortedMap: getting value for largest key less or equal a given value...

I've got an approach like the following, but I'm not entirely
happy with it. (see embedded comments)
Error checking left out only for brevity-of-post's sake.

<sscce>
class StepFunction<K,V> {
   SortedMap<K,V> m_map = new TreeMap<K,V>();
   public void put(K k,V v) { m_map.put(k,v); } // for demo-fill
   
   /** @return the value for the largest key in the map
          that is less OR equal to the given parameter. */

   public V value(K k) {
      // not really correct for generic use. In my usecase, K is
      // actually Long, so I just add one to k to make it work.
      return m_map.get(m_map.headMap(k).lastKey());

      // I'm a bit unhappy about headMap's "open end",
      // and also about the lack of some method like
      // lastEntry() or lastKeysValue() in SortedMap,
      // requiring one to look up the lastKey in the map,
      // although the map had "its finger on it" just before.
      // Did I miss something simple and obvious?
   }
   // demo-helper
   void checkVal(K k, V v) {
      System.out.println( map.value(k) + " should be " + v);
   }
   public static void main(String[] args) {
      StepFunction<Integer,Double> sf = new StepFunction<>()
      sf.put(Integer.MIN_VALUE, -1.0);
      sf.put(0, 0.0); sf.put(2, 1.0);

      sf.checkVal(-1 , -1.0);
      sf.checkVal( 0 , 0.0);
      sf.checkVal( 1 , 0.0);
      sf.checkVal( 2 , 1.0);
      sf.checkVal(Integer.MAX_VALUE , 1.0);
   }
}
</sscce>

PS: No need to offer "solutions" involving linear search.
  I could have come up with one, myself, if I wanted one.