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;
long long w[1000000], w1[100000];
long long t[1000000];
pair<long long, long long> ans;
long long a, b, c, n, m, q, k, x, c1, b1;
long long poww(long long x, long long y) {
  if (x == 0) return 0;
  if (x == 1) return 1;
  if (y == 0) return 1;
  if (y == 1) return x;
  long long d = poww(x, y / 2);
  if (y % 2) return d * d * x;
  return d * d;
}
map<long long, long long> M;
vector<long long> v;
int main() {
  cin >> a >> b >> c;
  for (int i = 1; i <= 1000000; i++) {
    a *= 10;
    if (a / b == c) return cout << i, 0;
    a %= b;
  }
  cout << -1;
  return 0;
}
