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. 
__author__ = 'smart131'
a, b, c = map(int, input().split())
r = a % b
u = []
for i in range (b):
    u.append ((10 * r) // b)
    r = (10 * r) % b

ans = -2
i = 0
while i < b:
    if u[i] == c:
        ans = i
        i += b
    i += 1
print(ans + 1)