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 = raw_input().split()
n = int(a[0])
d = int(a[1])
c = int(a[2])
f = [0]*d
count = 0
flag = 0
n *= 10
while(count<=d):
    if(d>n):
        if(c == 0):
            print str(count+1)
            flag = 1
            break
        count += 1        
        n*=10
    else:
        count += 1
        
        g = n/d
        
        if(g == c):
            flag = 1
            print str(count)
            break
        
        else:
            r = n%d
            if(f[r-1]==1):
                break
            f[r-1] = 1
            if(r == 0):
                if(c==0):
                    flag = 1
                    print str(count+1)
                break
            
            n = r*10

if(flag==0):
    print "-1"
    
    
