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. 
split_strings = input().split()
[a, b, c] = map(lambda x: int(x), split_strings)

seen_so_far = set()

remainder = (a % b) * 10
position = 1

while True:
    digit = remainder // b
    remainder %= b

    if digit == c:
        print(position)
        exit(0)

    if remainder in seen_so_far:
        print(-1)
        exit(0)

    seen_so_far.add(remainder)
    remainder *= 10
    position += 1

