# 3382. Multiplying Digits

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: $f_3(80) = 16$.

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 $f_B(X) = N$?

### 输入格式

The input consists of a single line containing two integers $B$ and $N$, satisfying $2 < B \leq 10~000$ and $0 < N < 2^{63}$.

### 输出格式

Output the smallest positive integer solution $X$ of the equation $f_B(X) = N$. If no such $X$ exists, output the word impossible. The input is carefully chosen such that $X < 2^{63}$ holds (if $X$ exists).

### 样例

Input
10 24

Output
38

Input
9 216

Output
546

Input
10 11

Output
impossible

Input
10000 5810859769934419200

Output
5989840988999909996


3 人解决，4 人已尝试。

3 份提交通过，共有 80 份提交。

8.4 EMB 奖励。