Carl Is Stopped at the U

Carl is stopped at the U.S.border between Mexico and the United States.Border patrol officers become suspicious about his contradictory answers about where he was in Mexico.They ask for consent to search and Carl refuses.The officers inform him that they have a drug-sniffing dog on hand,who can sniff out illegal narcotics.They again ask for consent and Carl again refuses.They bring in the dog who immediately scratches at Carl's spare tire.This is how the dog indicates the presence of illegal narcotics.They open the tire and find a kilo of cocaine.Is this a valid search?

A) No,because there was no legal basis for the use of the dog.
B) No,because the search was carried out over Carl's objection.
C) Yes,because there was a valid consent.
D) Yes,because there was sufficient probable cause after the dog scratched at the tire.