We are traveling from Chicago to Madrid (with a layover in Lisbon). Once we are in Madrid, we have a long layover before continuing to Las Palmas, Spain on a different airline. We are not checking any luggage. We will check-in for both flights before we leave home. When we are in Madrid, do we need to go out through security to the check-in desk for the different airline or can we go straight to the gate and let them know we have arrived?