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. 

if __name__=="__main__":
    a,b,c=map(int,raw_input().split())
    it=1
    fg=1
    while it<=100000:
        a%=b
        i=0
        f=0
        while a<b:
            if a==0:
                break
            a*=10
            i+=1
            if i>1:
                if c==0:
                    print it
                    f=1
                    break
                it+=1
        if f:
            fg=0
            break
        if c==a/b:
            print it
            fg=0
            break
        it+=1
    if fg:
        print "-1"
