You have a fraction <image>. 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: <image>. The first zero stands on second position.

The fraction in the second example has the following decimal notation: <image>. There is no digit 7 in decimal notation of the fraction. 
#include <bits/stdc++.h>
using namespace std;
priority_queue<pair<long long int, int> > pq;
vector<pair<int, int> > vp;
map<long long int, int> mp, m;
const int N = 1e5 + 6;
long long int ans[N];
vector<int> v, v1;
set<long long int> s, s1;
int visit[N];
struct domingo {
  int val, left, right;
} o[N];
bool used[102];
int main() {
  int a, b, c, ct = 1;
  cin >> a >> b >> c;
  a = a % b;
  a *= 10;
  for (int i = 0; i < 1e5 + 5; i++) {
    int x = a / b;
    a %= b;
    if (x == c) return cout << ct, 0;
    a *= 10;
    ct++;
  }
  cout << -1;
}
