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().strip().split(' '))
rem = a % b
if(rem == 0):
	if(c == 0):
		print 1
	else:
		print -1
remainders = {}
position = None
count = 0
a = a % b
while position is None:
	count += 1
	if(a < b):
		a *= 10	
	q = a / b
	a = a % b
	if(q == c):
		position = count
		break
	try:
		remainders[a]			
		break
	except:
		remainders[a] = True
if(position):
	print position
else:
	print -1
		
	