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())
s = []
while a != 0:
    t = 0
    while a < b:
        if t == 1:
            s.append([0, 0])
            if c == 0:
                print(len(s))
                exit(0)
        a *= 10
        t = 1
    d = a // b
    a %= b
    if [d, a] in s:
        print(-1)
        exit(0)
    elif d == c:
        print(len(s) + 1)
        exit(0)
    s.append([d, a])
    if a == 0 and c == 0:
        print(len(s) + 1)
        exit(0)
print(-1)
        
    
