A binary Huffman code is used for encoding symbols $1, \ldots, m$ occurring with probabilities $p_{1} \geqslant \ldots \geqslant p_{m}>0$ where $\sum_{1 \leqslant j \leqslant m} p_{j}=1$. Let $s_{1}$ be the length of a shortest codeword and $s_{m}$ of a longest codeword. Determine the maximal and minimal values of $s_{1}$ and $s_{m}$, and find binary trees for which they are attained.