As a programmer, you are probably familiar with the binary representation of integers. That is, write an integer $x$ as $\sum a_{i}2^{i}$, where each $a_{i}$ is either $0$ or $1$. Particularly, $n$-digit binary number can be written as $\sum_{i = 0}^{n-1} a_{i}2^{i}$, in which $a_{n-1}$ must equal to $1$.
This time, to test your mastery of binary numbers, Leg Han raises a problem to you.
Among all $n$-digit binary numbers whose amount of $1$ is $m$, please print the $k$-th smallest one.
It is guaranteed that k is legal.
