Impossible guess: AI

Meet BINNFR the ai(BINary Number FindeR)

A dialogue game, where you(or AI) can pick a number while the other will try to guess it. But you have also a limited chance (11 guesses in 0 to 2000).

But the AI never fails to find it(Even if you cheat).

Rules:

• You(or ai) can only input numbers.
• If the answer is is no, you have to tell whatever the right answer is bigger or smaller.