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]=raw_input().split(' ')
a=int(a)
b=int(b)
c=int(c)
found=0
for x in xrange(1,1000):
    v=a
    for y in xrange(0,x):
        v=v*10
    v=v/b
    v=v%10
    #print v,x
    if (v==c):
        print x
        found=1
        break
        
if not found:
    print -1