Write a Turing machine that converts its input from binary to unary. In other words, if the input is the string x ? {$, 0, 1} * , a $ followed by the binary expansion of the nonnegative integer n (for example, $101 to represent n = 5), then the machine outputs the string 1n (e.g., 15 = 11111). You may assume the input string will be in this format, i.e., a $ followed by either just a 0, or followed by a binary string beginning with 1.