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())

if a > b:
    a = a%b

position = 0
remainders = set()
f = 0

while f==0 and a not in remainders and a != 0:

    remainders.update({a})

    while a < b:
        a = a*10
        position += 1

        if a < b and c == 0:
            print position
            f = 1
            break


    if f == 0 and a/b == c:
        print position
        f = 1
        break
    else:
        a = a%b

if a == 0 and c == 0:
    print position+1

elif f == 0:
    print -1