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,b,c=int(a),int(b),int(c)
rem1=-1
flag=0
count=0
d=a%b
while d!=rem1 and count<=1000000:
    rem1=d%b
    count+=1
    d=d*10
    q=d//b
    if q==c:
        print(count)
        flag=1
        break
    d=d%b
if flag==0:
    print(-1)
    
        
        
