Separate exponentials

Question

Good afternoon, I have an expression

Exp[2 I (t - tau) + a] + 2 Exp[2 I t + b] + 3 Exp[-I t + b]

And I want to write it as a summation of powers of Exp[I t]. So,

3 Exp[b] Exp[-I t] + Exp[2 I t] (2 Exp[b] + Exp[a - 2 I tau])

What is the way to do this? I had several attempts including

Collect[%, Exp[I t]]

But that gives me only part of what I need:

3 Exp[b - I t] + Exp[2 I t] (2 Exp[b] + Exp[a - 2 I tau])

Thanks in advance!