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 = map(int, input().split())
N = 100000
MUL = int(1e6)

pos = 0
can = False
c = str(c)

for i in range(N):
    a *= MUL
    
    s = ("%.6f" % (a // b / MUL))
    point = s.find(".")
    s = s[point + 1:]
    
    a = a % b
    cur_p = s.find(c)
    
    if cur_p == -1:
        pos += len(s)
    else:
        can = True
        pos += cur_p
        break

if can:
    print(pos + 1)
else:
    print(-1)