A recipe that makes $5$ servings of hot chocolate requires $2$ squares of chocolate, $\frac{1}{4}$ cup sugar, $1$ cup water, and $4$ cups milk. Jordan has $5$ squares of chocolate, $2$ cups of sugar, lots of water, and $7$ cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make? Express your answer in the form of an improper fraction \frac{k}{m}, and find the value of k + m.

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