The smallest multiple#4459
Given a number and a set of digits .
Your task is to append the minimum number of digits from to so that the resulting number is divisible by . The resulting number should be the smallest possible.
The first line of the input contains two natural numbers and (1 \leq X \leq 10^{1000}, 2 \leq k \leq 100000). The second line contains the number of digits in the set . The third line lists these digits separated by spaces.
Output a single line containing the smallest number obtained from by appending digits from that is divisible by . If no such number can be formed, output .
Example 1