Which one of us "asked out the other?"

There's this girl at school that I've really only met in person briefly a couple of times this past semester. Anyway, we were recently talking on Facebook, and she suggested that we go get some coffee together (we all know what that means) and she came up with the time. I came up with the place where we'd go. Anyway, I feel that there are different protocols for paying on dates depending on who asked out the other. However, since she asked me out and came up with a time while I came up with a place, I'm not sure how we should pay. Based on what happened, who should be considered the one who asked out the other?
Which one of us "asked out the other?"
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