SP27096 FN16BASE - Forever Young

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 $ .

Multiple test cases. Please process until EOF is reached. Each test case 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 $ ).

For each test case, display the largest base $ b $ as described above in a single line.