My birthday is coming up. Alas, I am getting old and would
like to feel young again. Fortunately, I have come up with an
excellent way of feeling younger: if I write my age as a number
in an appropriately chosen base $b$, then it appears to be smaller.
For instance, suppose my age in base $10$ is $32$. Written in base $16$ it is only $20$!
However, I cannot choose an arbitrary base when doing this.
If my age written in base $b$ contains digits other than
$0$ to $9$, then it will be obvious that I am
cheating, which defeats the purpose. In addition, if my age
written in base $b$ is too
small then it would again be obvious that I am cheating.
Given my age $y$ and a
lower bound $\ell $ on how
small I want my age to appear, find the largest base
$b$ such that $y$ written in base $b$ contains only decimal digits, and
is at least $\ell $ when
interpreted as a number in base $10$.
Input
The input consists of a single line containing two base 10
integers $y$ ($10 \le y \le 10^{18}$ – yes, I am
very old) and $\ell
$ ($10 \le \ell \le
y$).
Output
Display the largest base $b$ as described above.
Sample Input 1 
Sample Output 1 
32 20

16

Sample Input 2 
Sample Output 2 
2016 100

42
