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. 

#Codeforces 900B
a,b,c=map(int,raw_input().split())

def gcd(a,b):
    while a>0:
        a,b=b%a,a
    return b


a,b=a/gcd(a,b),b/gcd(a,b)

def num(a,b,c):
    v=[]
    i=0
    while a not in v:
        v.append(a)
        t=10*a/b
        if t==c:
            return i+1
        a=10*a%b
        i+=1
    return -1


print num(a,b,c)





