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2018-2019 ICPC, NEERC, Southern Subregional Contest (Online Mirror, ACM-ICPC Rules, Teams Preferred) |
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Finished |

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A. Find a Number

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

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