Find a Number

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 ≤ d ≤ 500, 1 ≤ s ≤ 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

inputFormat

Input

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

outputFormat

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

样例

15 50

-1