We call a natural number a duodigit if its decimal representation uses no more than two different digits. For example, $12$, $110$ and $33333$ are duodigits, while $102$ is not.
It can be shown that every natural number has duodigit multiples. Let $d(n)$ be the smallest (positive) multiple of the number $n$ that happens to be a duodigit. For example, $d(12)=12$, $d(102)=1122$, $d(103)=515$, $d(290)=11011010$ and $d(317)=211122$.

Let ${\displaystyle D(k)=\sum _{n=1}^{k}d(n)}$. You are given $D(110)=11047$, $D(150)=53312$ and $D(500)=29570988$.

Find $D(50000)$. Give your answer in scientific notation rounded to $13$ significant digits ($12$ after the decimal point). If, for example, we had asked for $D(500)$ instead, the answer format would have been 2.957098800000e7.