Find The Multiple

Description

Given a positive integer n, write a program to find out a nonzero multiple m of n whose decimal representation contains only the digits 0 and 1. You may assume that n is not greater than 200 and there is a corresponding m containing no more than 100 decimal digits.

Input

The input file may contain multiple test cases. Each line contains a value of n (1 <= n <= 200). A line containing a zero terminates the input.

Output

For each value of n in the input print a line containing the corresponding value of m. The decimal representation of m must not contain more than 100 digits. If there are multiple solutions for a given value of n, any one of them is acceptable.

Sample Input

2
6
19
0

Sample Output

10
100100100100100100
111111111111111111

Source

Dhaka 2002

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int n;
int flag;
int dfs(unsigned long long s,int step)
{
    if(flag==1||step==19)
        return 0;
    else if(s%n==0)
    {
        printf("%I64u\n",s);
        flag=1;
        return 1;
    }
    else
    {
            if(!dfs(s*10,step+1))
        dfs(s*10+1,step+1);
    }
}
int main()
{
    while(~scanf("%d",&n)&&n)
    {flag=0;
        dfs(1,0);

    }
    return 0;
}