You are given two positive integers $d$ and $s$. Find minimal positive integer $n$ which is divisible by $d$ and has sum of digits equal to $s$.

Input

The first line contains two positive integers $d$ and $s$ ($1 \le d \le 500, 1 \le s \le 5000$) separated by space.

Output

Print the required number or -1 if it doesn't exist.

见题面 Input 部分

见题面 Output 部分