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 = 10000

def is_good(num):
    while num % 2 == 0:
        num //= 2
    while num % 5 == 0:
        num //= 5

    return num == 1

a, b, c = map(int, input().split())

a %= b

c = str(c)
flag = False

s = str(Decimal(a) / Decimal(b))[2:]
if is_good(b):
    s = s + "00"

for i, d in enumerate(s[:-1]):
    if d == c:
        print(i + 1)
        flag = True
        break

if not flag:
    print(-1)
