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=map(int,input().split())
a=(a%b)
count=0
l=0
m=0
n=0
k=0
while True:
    n=a
    a*=10
    k=a//b
    a=(a%b)
    count+=1
    if k==c:
        l+=1
        print(count)
        break
    if a==0 and c!=0 :
        m+=1
        break
    if n==k and c==k:
        print(count-1)
        break
    if n==a:
        m+=1
        break
    if count>b:
        m+=1
        break
if m>l:
    print('-1')