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, raw_input().split())

d = {}
idx = 0
findit = False
while True:
    a *= 10
    idx += 1
    curr_digit = a / b
    a = a % b
    if curr_digit == c:
        findit = True
        break

    key = str(curr_digit) + '_' + str(a)
    if key in d:
        break
    else:
        d[key] = 1
    

if findit:
    print idx
else:
    print -1
    
