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())
a %= b
if a == 0:
    if c == 0:
        print(1)
    else:
        print(-1)
    exit()
p = 0
h = set()
#while a*10 < b:
#    a *= 10
#    p += 1
ans = -1
while 1:
    a *= 10
    p+=1
    nm = a // b
    if nm == c:
        ans = p
        break
    if a - b*nm in h:
        break
    h.add(a - b*nm)
    a = a - b*nm
print(ans)