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. 
x=raw_input().split(' ')
a=int(x[0])
b=int(x[1])
c=int(x[2])

ctr=1
save=-1
while ctr<500000:
    r=a%b
    if r==0:
        if c==0:
            save=ctr
        break
    d=(r*10)/b
    if d==c:
        save=ctr
        break
    a=r*10
    ctr=ctr+1
print save
