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. 
def convert(numerator, denominator):
    ans= str(numerator//denominator)+ "."
    l={}
    index=0
    numerator = numerator%denominator
    l[numerator]=index
    t=False
    while t==False:
        if numerator==0:
            break
        digit = numerator*10//denominator
        numerator=numerator*10-(numerator*10//denominator)*denominator
        if numerator not in l:
            ans+=str(digit) 
            index+=1
            l[numerator]=index
            t=False
        else:
            ans+=str(digit)+")"
            ans=ans[:l.get(numerator)+len(ans[:ans.index(".")+1])]+"("+ ans[l.get(numerator)+len(ans[:ans.index(".")+1]):]
            t=True
    return ans

n = raw_input().split(' ')
n = [int(i) for i in n]
a = n[0]
b = n[1]
c = n[2]
res = -1
f = 0
j = 1
k = a / b
drob = ""
s = convert(a, b)
if s.find("(") == -1:
    s = s + "0"
s = s.replace("0.", "")
s = s.replace("(", "")
res = s.find(str(c))
if res <> -1: res = res + 1
print res
