An architect and/or engineer furnishing design or contract administration services to an owner, contractor, subcontractor, materialman or furnisher for the improvement of real property shall be entitled to payment in accordance with part 2 of this chapter, if the architect and/or engineer contracts in writing with the owner; or in accordance with part 3 of this chapter, if the architect and/or engineer contracts in writing with a contractor, subcontractor, materialman or furnisher.