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())
counter = 0
ans = -1
n = len(str(a))+1
rests = set()
while True:
    counter += 1
    a = a * 10
    d = a / b
    if d == c:
        ans = counter
        break
    a = a - d * b
    if counter > n:
        if a not in rests:
            rests.add(a)
        else:
            break
print ans