Multiple

Write a program that, given a natural number N between 0 and 4999 (inclusively), and M distinct decimal digits X₁,X₂...X_M (at least one), finds the smallest strictly positive multiple of N that has no other digits besides X₁,X₂...X_M (if such a multiple exists).

Input

The input file has several data sets separated by an empty line, each data set having the following format:

• On the first line - the number N

• On the second line - the number M

• On the following M lines - the digits X₁,X₂...X_M.

Output

For each data set, the program should write to standard output on a single line the multiple, if such a multiple exists, and 0 otherwise.

Sample Input

22

3

7

0

1

2

1

1

Sample Output

110

0