Codeforces Round #450 (Div. 2) B. Position in Fraction【数论/循环节/给定分子m 分母n和一个数c，找出c在m/n的循环节第几个位置出现，没出现过输出-1】

B. Position in Fraction

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You have a fraction . You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

Input

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Output

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

Examples

input

1 2 0

output

2

input

2 3 7

output

-1

Note

The fraction in the first example has the following decimal notation: . The first zero stands on second position.

The fraction in the second example has the following decimal notation: . There is no digit 7 in decimal notation of the fraction.

 【题意】：给定分子m 分母n和一个数c，找出c在m/n的循环节第几个位置出现，没出现过输出-1。

【分析】：模拟实现循环节，记录出现过的下标。

【代码】：

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
const int maxn = 1e5+1000;
int i,pos=-1,c;
int main()
{
    int n,m,i;
       scanf("%d%d%d",&m,&n,&c);
       i=0;
       int cnt=0;
       int fz=m,fm=n;
       while(1)
       {
            i++;
            fz=fz*10;
            //printf("%d",fz/fm);
            if(fz/fm==c)
            {
                pos=i;
                break;
            }
            fz=fz%fm;
            if(i>=100005) break; //限制循环节长度
       }
       printf("%d\n",pos);
   return 0;
}