7. The Brazilian IMO leader chooses two natural numbers $n$ and $k$ with $n>k$, and then tells these to his deputy and a participant. The leader then whispers a binary sequence of length $n$ into the deputy's ear. The deputy writes down all binary sequences of length $n$ that differ from the leader's sequence at exactly $k$ positions. (Example for $n=3$ and $k=1$: If the leader chooses 101, the deputy writes down 001, 100, 111.) The participant looks at the sequences written down by the deputy. Now the participant tries to guess the original sequence from the leader.

How many times does he need to guess at minimum (depending on $n$ and $k$) to ensure he guesses correctly at least once?