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Is it okay to prospect my customer's customers?

Here is the situation: I have been working full-time for a customer (let's call him A) over the last month and most of this time was actually spent on projects from a single customer of them (let's call him B).

Now that I'm planning to launch a company that will be in direct competition with A, I'm wondering if I could tell B about it, give business cards and so on. How would that be perceived?