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().strip().split())
a%=b
save=a
a=a*10**1000//b
len=0
pos=-1
while a>0:
    if a%10==c:
        pos=len
    a//=10
    len+=1
if (save*10<b) and c==0:
    print(1)
else:
    print(1000-pos if pos!=-1 else -1)

        