Position in Fraction （小数除法模拟）

Position in Fraction

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.

code：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
int main(){
    int n,m,c,i;
    scanf("%d%d%d",&m,&n,&c);
    int pos = -1;
    int fz = m,fm = n;
    i = 0;
    while(1){
        i++;
        fz *= 10;
        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;
}