13468번 - Multiplying Digits 다국어

For every positive integer we may obtain a non-negative integer by multiplying its digits. This defines a function f, e.g. f(38) = 24.

This function gets more interesting if we allow for other bases. In base 3, the number 80 is written as 2222, so: f3(80) = 16.

We want you to solve the reverse problem: given a base B and a number N, what is the smallest positive integer X such that fB(X) = N?

The input consists of a single line containing two integers B and N, satisfying 2 < B ≤ 10 000 and 0 < N < 2⁶³.

Output the smallest positive integer solution X of the equation fB(X) = N. If no such X exists, output the word “impossible”. The input is carefully chosen such that X < 2⁶³ holds (if X exists).