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 *

context = Context(prec=10000)
setcontext(context)

a, b, c = map(int, input().split())
string = str(Decimal(a)/Decimal(b))

flag, ans = 0, 0
for i in range(len(string)):
    if string[i]==".":
        flag = 1
    elif flag==1:
        ans+=1
        if string[i]==str(c) and i<9999:
            print(ans)
            flag=-1
            break
if Decimal(float(string))*Decimal(b) == a and c==0:
    print(ans+1)
elif flag==1:
    print(-1)
