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. 
a, b, c = map(int, raw_input().split())


def find_digits(a, b, depth = 5):
  for d in range(10):
    if b * (d + 1) > a:
      first_digit = d
      break
    if b * (d + 1) == 0:
      return [d + 1, 0, 0]
  if depth == 0:
    return [first_digit]
  return [first_digit] + find_digits(10 * (a - first_digit * b),
                                     b,
                                     depth - 1)

digits = find_digits(a, b, depth=400)[1:]
if c in digits:
  print digits.index(c) + 1
else:
  print "-1"
