Neither. History does not belong to any one country, especially when the lines between them are remarkably recent. But thats hardly satisfying, so I will attempt to explain myself.

The IVC began around 3000 BCE and reached their peak in the mid 3rd millennium BCE, with major locations dotting the Indus river ant its tributaries and being a major trade partner with Sumer. By the end of the 3rd millennium, however, the IVC entered a slow decline which itself ended around 1400 BCE when their sites seemed to have been completely abandoned. We don't know exactly why they declined, but a few theories have been put forth.

The earliest theory emerged shortly after discovery and posited that the nomadic Indo-Aryans subjugated the IVC people and destroyed their cities. This has largely been dismissed due to more understanding over the movements of both cultures. Disease due to overpopulation has been a popular theory, as has famine. Recent finds in graves have led to the discovery of large amounts of bodies with wounds and practices consistant with internal violence and have indicated a sharp contrast between elites and others, perhaps indicating an increase in internal conflict. Those last three are not remotely mutually exclusive and are, in my opinion, complementary.

Next we need to talk about India and Pakistan. Historically, they -as well as some of Afghanistan- were considered part of India. By 1400 BCE, the Indo-Aryans established themselves in the Punjab before moving down the Indus and east towards the Gangetic plain. By 1000 BCE Indo-Aryans dominated the Northern part of the subcontinent. As time passed, an idea of the subcontinent as a unified region developed along with the idea of a Chakravatin, a person who ruled the entire "continent" of South Asia. While the idea existed before, the model was probably set by Ashoka Maurya, who ruled from Sindh to Arkan and Kashmir to Tamil Nadu. Notably, this was not all of what was considered Bharata, (or Jambudvipa as Ashoka called it) but it was the closest to unification before the British Raj, though the Guptas, the Tughlaqs, and the Mughals came close.

The area which is now Pakistan only began to diverge culturally from the majority of India during the late middle ages under influence from the Persian and Turkish dynasties that ruled and brought Islam to India. However, Indian Muslims on both sides of the current border remained quite similar culturally and considered themselves of the same group. The idea of a separate state, of Pakistan, did not exist until the late 19th century with the ascention of the "two-nation" theory, which eventually led to the partition. It was the partition that led to an increased divide, due to the exodus of Hindus and Sikhs from Pakistan and the Muslims to India. Of course, Muslims still remain in India, 189 million or 15% in fact, and there are a few Hindus and Sikhs in Pakistan. Countries change and new ethnicities and nationalities emerge, and I am not sure that this is the right place to go into the complex process of ethnogenesis and the anthropological and philosophical debates around it. What I'm trying to say, is that Pakistan and India are vastly more similar than they are different and arguments of something from their shared past "belonging" to one or the other is only good for stirring conflict.