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. 
import decimal

d_context = decimal.getcontext()
d_context.prec = 1000000
a, b, c = input().split()
a = decimal.Decimal(a)
b = decimal.Decimal(b)
s = str(a/b)
# print(s)
ans = -1

try:
    idx = s.index(".")
    if len(s) < 1000000 - 2:
        s = s + "00"
    for i in range(idx + 1, len(s) - 1):
        if s[i] == c:
            ans = i - idx
            break

except:
    pass
print(ans)


