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
decimal.getcontext().prec = 500

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

div = decimal.Decimal(a) / decimal.Decimal(b)
div = str(div)
dec = div.find('.')
after_dec = div[dec + 1 :]
if(len(after_dec) != 500):
    after_dec = after_dec + '0'
pos = after_dec.find(c)

if(pos == -1 or pos == 499):
    print(-1)
else:
    print(pos + 1)
