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>
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize(2)
#pragma G++ optimize(2)
using namespace std;
constexpr long long N = 2e5 + 9;
constexpr long long M = 400 + 9;
constexpr long long INF = 0x3f3f3f3f3f3f3f3f;
constexpr long long INF2 = 0xcfcfcfcfcfcfcfcf;
long long a, b, c;
unordered_set<long long> vis;
signed main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  ;
  cin >> a >> b >> c;
  long long pos = 0;
  a *= 10;
  while (a && vis.find(a) == vis.end()) {
    long long d = a / b;
    vis.insert(a);
    ++pos;
    if (d == c) {
      cout << pos << endl;
      return 0;
    }
    a = a % b * 10;
  }
  if (!a && !c) {
    cout << ++pos << endl;
  } else
    cout << -1 << endl;
  return 0;
}
