Chef and a Beautiful Digit

Chef Leonardo has a decimal integer $N$ and a non-zero decimal digit $d$. $N$ does not contain the digit zero; specifically, $N$ should always be treated as a decimal integer without leading zeroes. Chef likes $d$ and does not like any other digit, so he decided to change $N$. He may apply the following operation any number of times (including zero): append the digit $d$ to the decimal represen