Suppose the letters $a, \,b, \,c, \,d, \,e, \,f$ have probabilities $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \frac{1}{32}$, respectively.
Which of the following is the Huffman code for the letter $a, \,b, \,c, \,d, \,e, \,f$?

$0$, $10$, $110$, $1110$, $11110$, $11111$

$11$, $10$, $011$, $010$, $001$, $000$

$11$, $10$, $01$, $001$, $0001$, $0000$

$110$, $100$, $010$, $000$, $001$, $111$