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(k) for k in raw_input().split(" ")]

d=set([])

a=a%b
res=0

while True:
    d.add(a)
    res+=1
    a*=10
    dd=a/b
    a=a%b
    if dd==c:
        break
    if a in d:
        res=-1
        break

print res
