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 = str(a)
p = 0
d = 0
r = 0
ans = 1
while p != len(a):
    while p != len(a) and d < b:
        d = int(str(d) + a[p])
        p += 1
    while d >= b:
        d -= b
if d == 0:
    if c == 0:
        print(1)
    else:
        print(-1)
else:
    while True:
        d *= 10
        k = 0
        while d >= b:
            k += 1
            d -= b
        if ans == 10 ** 5:
            print(-1)
            break
        if k == c:
            print(ans)
            break
        ans += 1
    
