Get values for keys within a range in Java

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Suppose I have a map in Java which looks like this:

{ 
 39:"39 to 41",
 41:"41 to 43",
 43:"43 to 45",
 45:">=45"
}

If the keys are in sorted order(either using treemap or linkedhashmap).Now if i try to get a value which is >=39 and <41.Then I should get the String "39 to 41".How do I do this efficiently?

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