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. 
# Hello World program in Python
    
a,b,c=map(int, input().split())
pos=0 
flag=False
while(pos<10000):
    pos+=1
    a=a*10
    q=int(a/b)
    #print(q)
    if(q==c):
        #print(q)
        flag=True
        break;
    a=a%b

if(flag):
    print(pos)
else:
    print(-1)