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=map(int,input().split())
c=str(c)
s=''
a%=b
a*=10
v=[a]
while True:
    s+=str(a//b)
    a%=b
    a*=10
    if c in s:
        print(s.find(c)+1)
        exit()
    if a in v:
        print(-1)
        exit()
    else:
        v.append(a)
