Please reason step by step, and put your final answer within \boxed{}.
A team leader of an IMO (International Mathematical Olympiad) team selects positive integers \( n \) and \( k \) (with \( n > k \)), and informs the deputy leader and participants of these choices. Subsequently, the team leader secretly tells the deputy leader a binary string of \( n \) digits. The deputy leader then writes down all binary strings of \( n \) digits that differ from the leader's string in exactly \( k \) positions (for example, if \( n=3 \) and \( k=1 \), and the leader selects 101 and tells the deputy leader, the deputy leader should write down \( 001, 111, 100 \)). The participants are allowed to see the deputy leader's strings and attempt to guess the leader's original string. Determine the minimum number of guesses (dependent on \( n \) and \( k \)) required to guarantee finding the correct string.
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