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())
cnt=0
l=[]
for i in range(b+3):
    l.append(0)
k=a%b
f=0
while l[k]==0:
    if k==0 and c==0:
        cnt+=1
        f=1
        break
    elif k==0:
        break
    i=0
    l[k]=1
    while k*(10**i)<b:
        i+=1
    k=k*(10**i)
    if i>1 and c==0:
        f=1
        cnt+=1
        break
    cnt+=i
    if k//b==c:
        f=1
        break
    k=k%b
if f==1:
    print(cnt)
else:
    print("-1")
