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>
int vis[1000005] = {0};
int main(void) {
  int A, B, C;
  scanf("%d%d%d", &A, &B, &C);
  int ans = -1;
  int cnt = 1;
  A *= 10;
  while (1) {
    if (vis[A]) break;
    vis[A] = 1;
    if (A / B == C) {
      ans = cnt;
      break;
    }
    A = (A % B) * 10;
    cnt++;
  }
  printf("%d\n", ans);
}
