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 GCC optimize("unroll-loops")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,popcnt,abm,mmx,tune=native")
#pragma GCC optimize("fast-math")
#pragma GCC optimize "-O3"
using namespace std;
const long long INF = 1e9;
const long long INFLL = 1e12;
const long long MOD = 1000000007;
void fast_io() {}
signed main() {
  fast_io();
  long long a, b, n;
  cin >> a >> b >> n;
  a %= b;
  a *= 10;
  for (long long i = 1; i <= b; i++) {
    if (a / b == n) {
      cout << i;
      return 0;
    }
    a %= b;
    a *= 10;
  }
  cout << -1;
  return 0;
}
