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 = (int(x) for x in input().split(' '))

res = '.'
for i in range(b):
    s = a // b
    d = a % b
    if s == 0:
        a = a*10
    if i != 0:
        res += str(s)
    a = d*10
    if s == 1 and d == 0:
        res += '0'
        break

if b == 2:
    res += '0'

print(res.find(str(c)))