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. 
import sys

a, b, c = map(int, sys.stdin.readline().split())

a = a % b

to_divide = set()

result = []

while True:
    a *= 10
    while a < b:
        a *= 10
        result.append(0)
        if c == 0:
            print len(result)
            sys.exit(0)

    if a in to_divide:
        print -1
        sys.exit(0)

    div = a / b
    result.append(div)
    to_divide.add(a)
    if c == div:
        print len(result)
        sys.exit(0)

    a = a % b
    if a == 0:
        break

if c == 0:
    print len(result) + 1
else:
    print -1

