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 *
p = 1000
getcontext().prec = p
a, b, c = raw_input().split(' ')
d = str( Decimal(a)/ Decimal(b)).split('.')[1]
if len(d) < p:
    if c=='0':
        if c in d:
            print d.index(c) + 1
        else:
            print len(d) + 1
    else:
        if c in d:
            print d.index(c) + 1
        else:
            print -1
    exit()
try:
    i = d[:-1].index(c)
    print i + 1
except:
    print -1

