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A. Find a Number
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Examples
Input
13 50
Output
699998
Input
61 2
Output
1000000000000000000000000000001
Input
15 50
Output
-1