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

有几种不同的思路bfs或是dfs都可以但没有找到最好的方法，这两种不论哪一种都会漏掉一些解

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
using namespace std;
bool vis=false;
int k;
void BFS(int n)
{
	long long t;
	queue<long long> q;
	while(!q.empty())
	{
		q.pop();
	}
	q.push(1);
	while(1)
	{
			t=q.front();
			if(t%n==0) 
			{
				printf("%d\n",t);
				return;
			}
			q.pop();
		q.push(t*10);
		q.push(t*10+1);
	}
}

void DFS(unsigned __int64 x,int n,int k){
	if(vis) return;
	if(x%n==0){
		printf("%I64u\n",x);
		vis=true;
		return;
	}
	if(k==19) return;
	DFS(x*10,n,k+1);
	DFS(x*10+1,n,k+1);
}
int main()
{
	int n;
	while(scanf("%d",&n)&&n)
	{
		//BFS(n);
		vis=false;
		DFS(1,n,1);
	}
	return 0;
}