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 = input().split()
a=int(a)
b=int(b)
c=int(c)
ans=-1
mn=10**3000
while 1:
    a*=10
    ans+=1   
    if a>=b:
        break
a=a*mn
a//=b
s=str(a)
k=len(s)
t=0
i=0
if c==0 and ans>0 :
    print(1)
else:
    while 1:
        if i==k:
            break;
        elif s[i]==chr(c+48):
            t=1
            print(i+ans+1)
            break
        i+=1;
    if t==0:
        print(-1)