MULTII - Yet Another Multiple Problem

no tags 

Given a positive integer N (1 <= N <= 10000) and some digits, find the smallest positive multiple of N whose decimal notation does not contain any of the given digits.

Input

Each test case contains two lines. The first line contains two integers N and m separated by a single space. The second line contains m digits separated by spaces. Input terminates by EOF.

Output

For each test case output its case number (starting from 1) and the answer in a single line, or "-1" (without quotes) if the answer doesn't exist.

Example

Input:
2345 3
7 8 9
100 1
0

Output:
Case 1: 2345
Case 2: -1

hide comments
devu: 2012-12-01 08:19:35

Could You Just tell me the maximum length of the answer which would be coming..

Getting Runtime Error on 2012-12-01 , And on 10-08-2013 ..it's Accepted...The question asked by me is foolish ..I admit admin ...No reason for so less submission..straight forward problem :D

Last edit: 2013-08-09 18:32:40
(Tjandra Satria Gunawan)(曾毅昆): 2012-11-21 17:48:31

Ok, I give up, this problem is too hard for me for now...
In case like this:
2791 9
0 2 3 4 5 6 7 8 9
answer is not -1 but answer is 1111111111111111111111111111111
so it's very large integer :-O


Added by:Fudan University Problem Setters
Date:2012-11-21
Time limit:4s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM/ICPC Regional Contest, Chengdu 2012