ONEZERO  Ones and zeros
Certain positive integers have their decimal representation consisting only of ones and zeros, and having at least one digit one, e.g. 101. If a positive integer does not have such a property, one can try to multiply it by some positive integer to find out whether the product has this property.
Input
Number K of test cases (K is approximately 1000);
in each of the next K lines there is one integer n (1 <= n <= 20000)
Output
For each test case, your program should compute the smallest multiple of the number n consisting only of digits 1 and 0 (beginning with 1).
Example
Input: 3 17 11011 17 Output: 11101 11011 11101
hide comments
yzs:
20201011 09:18:22
simple bfs to consider all possible permutations of 0 and 1, starting with 1. :) 

knight_27:
20200627 01:56:52
it is beautiful to understand a proof that an answer always exists 

nandadeep_2001:
20200612 13:16:16
can anyone explain the algorithm


cpp219:
20200530 16:06:17
ez from LMH 

aryan__0406:
20200507 23:48:13
Good Question. Worth it! 

aryan__0406:
20200506 20:47:27
Every number till 20000 don't have such property such as 8.So in test cases only those numbers will be given which are valid.So chill! 

cheesy:
20200428 15:28:44
Is it guaranteed that an answer will exist?


ajaygupta007:
20200408 10:31:07
1.learn how to compute mod of a big number using string.


abhinav_jain02:
20200311 08:33:21
A really good question to attempt.


fran_1024:
20191117 21:46:57
You don't need long division, you can simply mod the whole time with the number in input and remember the actual number only as a string and when the modded number becomes zero you return the string. 
Added by:  PaweÅ‚ Dobrzycki 
Date:  20050526 
Time limit:  8s 
Source limit:  4096B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  II Polish Olympiad in Informatics, Ist Stage 