Let \(f_n\) be the \(n\)th Fibonacci number such that \(f_1=f_2=1\) and \(f_k=f_{k-1}+f_{k-2}\) for \(k \ge 3\). Is it possible that

\[f_x+f_{x+1}+f_{x+2}+f_{x+3}+f_{x+4}+f_{x+5}+f_{x+6}+f_{x+7}=f_{y}\]

where \(x\) and \(y\) are positive integers?

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