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. 
from decimal import *
getcontext().prec = 505

a, b, c = [int(i) for i in input().split()]
r = Decimal(a) / Decimal (b)
r = list(str(r))
if len(r) < 405:
    for i in range(3):
        r.append(str(0))
r = r[1:-1]
for i in range(len(r) - 2):
    if r[i + 1] == str(c):
        print(i + 1)
        exit(0)
print(-1)


