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=input().split()
a=int(a)
b=int(b)
c=int(c)
l=[]
rem=a
while rem*10//b==0:
	ans=rem*10//b
	l.append(ans)
	rem=rem*10%b
nz=rem*10//b
l.append(nz)
rem=rem*10%b
for i in range(1001):
	ans=rem*10//b
	rem=rem*10%b
	l.append(ans)
#print(l)
j=1
find=False
for i in l:
	if c==i:
		print(j)
		find=True
		break
	j+=1
if not find:
	print(-1)