Examine the following statements related to the integration of Princely States into the Union of India post-independence and identify the correct statements from the options given below:

A) Sardar Vallabhbhai Patel, the then Deputy Prime Minister of India, played a pivotal role in the integration of Princely States into the Union of India through a policy of diplomacy and, if necessary, force.

B) The Instrument of Accession was a legal document created for Princely States to accede to the Indian Union, which specified that the State would cede control over defence, foreign affairs, and communications to the Indian government.

C) Hyderabad, under Nizam's rule, willingly joined the Indian Union immediately after independence without any resistance or military intervention.

D) The integration process of Princely States was completed immediately after India gained independence in 1947, without any states resisting accession.