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;
map<int, bool> mp;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  int a, b, c, d, e;
  scanf("%d%d%d", &a, &b, &c);
  d = gcd(a, b);
  a /= d;
  b /= d;
  d = a / b;
  a -= d * b;
  a *= 10;
  int rel = -1;
  for (int i = 1; i < b + 1; i++) {
    d = a / b;
    a -= d * b;
    if (d == c) {
      rel = i;
      break;
    }
    a *= 10;
  }
  if (rel == -1)
    printf("-1\n");
  else
    printf("%d\n", rel);
  return 0;
}
