Alan wants a new phone password but he's rather picky.
Firstly, he wants the password to contain ~5~ digits. Secondly, he wants the sum of the digits to equal ~X~. Thirdly, he wants the product of the digits to equal ~Y~. Finally, he does not want the password to contain the digit ~0~.
Please help Alan find the lexicographically smallest password that satisfies his conditions.
The first line and only line will contain two space-separated integers, ~X (5 \le X \le 45)~ and ~Y (1 \le Y \le 59049)~.
Output the lexicographically smallest password that satisfies Alan's conditions. It is guaranteed that a solution exists.
23145 etc. also satisfy Alan's requirements, but
12345 is the lexicographically smallest solution.