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<p>You are building a diving board by placing a bunch of planks of wood end-to-end. There are two types of planks, one of length <code>shorter</code> and one of length <code>longer</code>. You must use exactly <code>K</code> planks of wood. Write a method to generate all possible lengths for the diving board.</p>
<p>return all lengths in non-decreasing order.</p>
<p><strong>Example: </strong></p>
<pre>
<strong>Input: </strong>
shorter = 1
longer = 2
k = 3
<strong>Output: </strong> {3,4,5,6}
</pre>
<p><strong>Note: </strong></p>
<ul>
<li>0 &lt; shorter &lt;= longer</li>
<li>0 &lt;= k &lt;= 100000</li>
</ul>