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 divide(x, y):
    a = []
    integer = []
    decimal = []
    while x > 0:
        a.append(x % 10)
        x = x // 10
    a.reverse()
    [a.append(0) for x in range(y)]
    k = 0
    for i, n in enumerate(a):
        k = k * 10 + a[i]
        p = 0
        while p <= k:
            p += y
        p -= y
        k = k - p
        if i <= len(a) - y - 1:
            integer.append(p // y)
        else:
            decimal.append(p // y)
    return integer, decimal
a, b, c = (int(x) for x in input().split())
integer, decimal = divide(a, b)
if c in decimal:
    print(decimal.index(c) + 1)
else:
    print(-1)
