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 hdiv(dividend, divisor, precision=0):

    a = dividend
    b = divisor

    if abs(a + b) == abs(a) + abs(b):
        flag = 1
    else:
        flag = -1

    a = abs(a)
    b = abs(b)

    quotient = a // b
    remainder = a % b

    if remainder == 0:
        return quotient

    ans = str(quotient) + '.'

    i = 0
    while i < precision:
        a = remainder * 10
        quotient = a // b
        remainder = a % b
        ans += str(quotient)
        if remainder == 0:
            break
        i += 1

    if precision == 0:
        ans = ans.replace('.', '')

    if flag == -1:
        ans = '-' + ans

    return ans
if __name__ == "__main__":
    a, b, c = map(int, input().split())
    s = str(hdiv(a, b, 100000)).split('.')[-1:]
    index = 0
    flag = False
    for item in s[0]:
        index += 1
        # print(str(item), str(int(c)))
        if str(item) == str(int(c)):
            print(index)
            flag = True
            break
    if flag is False and index < 9 and int(c) == 0:
        print(index + 1)
        flag = True
    if flag is False:
        print(-1)

