Firstly, there's only one Buddha who was born in Lumbini in the ancient "Indian" kingdom of Kapilvastu. When we say India is very old, we mean India as a civilization is very old not necessarily a political union. Nepal was a part of Indian civilisation. Modern political boundaries of 1947 did not apply back then. It was all about who had influence and whose culture dominated.
Secondly, Pakistan as a concept came in 1930 and as a country came in 1947. All that was before then was India. Indus-Saraswati civilisation was an Indian civilisation. Aryans did not enslave our kind, we are ourselves descendants of Aryans as almost all speakers of Indo-Iranian languages are. Every thing that occurred in what is now Pak b4 1947 is said to have occured in India. Your own ancestors called themselves Bhartis, the descendants of Bharat.
Even professional historians from neutral countries will laugh if you'll say Dharmic faith are not Indian in origin!
Well dharmic faiths are not purely indian. They are indo-chinese in origin . Even Confucianism,taoism ,zen buddhism,bon ,dzogchen and chinese animism have huge dharmic concepts like reincarnation,karma .
And there is buddha padmasambhava in tibetan buddhism