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;
const long long PI = 3.1415926535897932384626433832795;
const long long INF = 8000000000000000000;
const long long mod = 1000000007;
const long long MOD = 1000000007;
const long long dx[] = {1, -1, 0, 0};
const long long dy[] = {0, 0, 1, -1};
const long long month[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long a, b, c;
  cin >> a >> b >> c;
  for (long long i = 1; i <= 10000; i++) {
    a *= 10;
    long long q = a / b;
    long long d = q % 10;
    long long r = a % b;
    if (d == c) {
      cout << i;
      exit(0);
    }
    a = r;
  }
  cout << -1;
  exit(0);
}
