Gabriel has two jars of jelly beans, one with x beans and the other with y beans. Each jar has a lever. When a jar has at least 2 beans, pressing its lever will give Gabriel one bean from it and move one bean from it to the other jar (if there are 1 or 0 beans in the jar, then pressing the lever has no effect). Determine necessary and sufficient conditions on x and y, so that Gabriel can extract all but one of the jelly beans.