题目描述

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 $10$.

输入格式

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 $\ell$ ($10 \le \ell \le y$).

输出格式

Display the largest base $b$ as described above.

题目大意

题目大意

我的生日快到了！唉，但如今我已经老了，我想重新获得年轻的感觉。

幸运的是，我想出了一个让人感觉更年轻的好方法：如果我把我的年龄以适当选择的$b$进制书写，那么它看起来会更小。例如，假设我以$10$进制书写的年龄是$32$岁；以$16$进制书写，它只有$20$($0x20$)！

然而，在这样做时，我不能选择任意进制数。如果以$b$进制为数写的我的年龄包含$0-9$以外的数字，那么很明显我在作弊，这违背了目的。此外，如果我的年龄的进制数$b$太小，那么很明显我在作弊。

在我希望我的年龄看起来有多小的问题上,考虑到我的年龄$y$和下限$l$，找到最大的进制数$b$，这样写在基数$b$中的$y$只包含十进制数字，并且当将其看做一个十进制数字时至少是$l$。

输入格式

输入由一行组成，其中包含两个$10$进制的整数$y$ ($10\le y\le10^{18}$ –是的,我很老）和$l$($10\le l \le y$)

输出格式

如上所述，输出最大进制数$b$。

说明/提示

时间限制：$1s$，内存限制：$1GB$

(洛谷这里实际是$512MB$,但原题是$1GB$)

$2016年$国际大学生编程大赛$ACM$-$ICPC$世界总决赛

32 20

16

2016 100

42

提示

Time limit: 1000 ms, Memory limit: 1048576 kB.

International Collegiate Programming Contest (ACM-ICPC) World Finals 2016