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=[int(i) for i in input().split()]
while a>b:
    a-=b*(a//b)
t=a/b
s=str(t)
count=1
while True:
    if 'e' in s:
        count+=1
        a=a*10
        while a>b:
            a-=b*(a//b)
        t=a/b;s=str(t)
    else:
        n=s.index('.')
        break
while int(s[n+1])!=c:
    count+=1
    a=a*10
    while a>b:
        a-=b*(a//b)
    t=a/b;s=str(t)
    n=s.index('.')
    if count>100005:
        count=-1
        break
print(count)
    

