How do I parse this piece of XML?

I have the following piece of XML in my SQL:

DECLARE @xml XML
SET @xml = '<?xml version="1.0" encoding="UTF-8"?>
<BillingAddresses>
  <BillingAddress Winner="W1">
    <Losers>
      <Loser Id="L1" />
      <Loser Id="L2" />
      <Loser Id="L3" />
    </Losers>
  </BillingAddress>
  <BillingAddress Winner="W10">
    <Losers>
      <Loser Id="L65" />
    </Losers>
  </BillingAddress>
</BillingAddresses>'

I'd like to fetch data in the following manner.

Winner | LoserID 
W1       L1
W1       L2
W1       L3
W10      L65

I can get to the Winner attribute of BillingAddress:

SELECT Col.value('(@Winner)[1]', 'varchar(30)')
FROM @xml.nodes('/BillingAddresses/BillingAddress') Rev(Col) 

but I am at a loss how to get to the Id attribute of the Loser nodes