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,raw_input().split())
arr=[]
a=10*a
count=0
while(a>0):
    while(10*a<b):
        arr.append(0)
        count+=1
        a=10*a
    arr.append(a/b)
    count+=1
    k=a%b
    a=(a%b)*10
    if k==0 or count>=100000:
        break
if count<100000:

    arr.append(0)
found=False
for i in range(len(arr)):
    if arr[i]==c:
        print i+1
        found=True
        break
if found==False:
    print -1



