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.

-----Examples-----
Sample Input:
32 20
Sample Output:
16

Source: kattis | Difficulty: HARD


Solutions: