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. 
#Abhigyan Khaund - syl
# n = int(raw_input())
a,b,c = (map(int, raw_input().split()))
l = 0
s = set([])
arr = []
zero = 0
ans = 1
while True:
	t = (a*10)/(b)
	arr.append(t)
	s.add(a*10)
	if(len(s)==l):
		break
	else:
		l+=1
	a = (a*10)%b
	if(a==0):
		zero = 1
		break
	ans+=1
k = 1
for i in arr:
	if(i==c):
		print k
		exit(0)
	k+=1
if(c == 0 and zero == 1):
	print ans+1
	exit(0)
print -1
