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 = list(map(int,input().split()))
rem = a%b
lf = {}
lf[rem]=True
div = rem*10//b
rem = (rem*10)%b
pdiv = div
if div != c:
    pos = 2
    output = -1
    while True:
        divn = rem * 10 // b
        if c == divn:
            output = pos
            break
        if lf.get(rem,False):
            break
        lf[rem] = True
        rem = (rem*10)%b
        pos+=1
    print(output)
else:
    print(1)