I joined the Eid prayers in first Rak`ah when the imam had already said 2 or 3 Takbirs. At that time I was…

I joined the Eid prayers in first Rak`ah when the imam had already said 2 or 3 Takbirs. At that time I was not sure that it’s the first Rak`ah or second, so I made the Niyyah & joined the prayer. Afterwards when the prayer proceeded I came to know that I joined the prayer in the first Rak`ah but had missed around 2 takbirs (& Qunuts). Is the prayer correct or not?