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. 
def encontrar(a,b,c):
    a = a%b
    for i in range (1,b+1):
        a = a*10
        if int(a/b) == c:
            return i
        a = a%b
    return -1

    #INICIO
fraccion = input()
fraccion = fraccion.split()

a = int(fraccion[0])
b = int(fraccion[1])
c = int(fraccion[2])
print(encontrar(a,b,c))
