Points \(A,B,C,D,E\) and \(F\) lie, in that order, on \(\overline{AF}\), dividing it into five segments, each of length \(1\). Point \(G\) is not on line \(AF\). Point \(H\) lies on \(\overline{GD}\), and point \(J\) lies on \(\overline{GF}\). The line segments \(\overline{HC}, \overline{JE},\) and \(\overline{AG}\) are parallel. Find the ratio \(\frac{HC}{JE}\). The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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