Google Sheets: how to find max value in column B, corresponding values in column A, and max among these

Question

I have two numeric columns, A and B. I want to find the max value in column B, which will return multiple rows. Then I want to find the max value in column A from among these rows.

A   B
 5  315
 7  315
10  275

The function should return:

 7  315

It would be fine if this were a combination of two functions - one that finds the max value in B (315), and another that finds the corresponding max value in A (7). That's how I'm trying it right now using:

=index(A2:B10,match(max(B2:B10),B2:B10,0))

But this solution only finds the latest row that has column B's max value:

 5  315

Someone suggested I use the query function, but I couldn't get that to work either.