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. 
numbers = [int(x) for x in raw_input().split()]

a = numbers[0]
b = numbers[1]
c = numbers[2]

a = a * 10

set = {a}

i = 1
while True:
    res_1 = a / b
    if res_1 == c:
        print i
        break

    mod_1 = a % b
    a = mod_1 * 10
    if a in set:
        print -1
        break
    else:
        set.add(a)

    i += 1