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())

fraction =''
for i in range(500):
	if (a == 0):
		fraction+='0'
		break
	a =a*10
	while True:
		if (a >= b):
			break
		a =a*10
		fraction+='0'
		'''
	reminder =int(a/b)
	fraction+=str(reminder)
	'''
	fraction+=str(int(a/b))
	a =a%b
#print (fraction)

c =str(c)
if (c in fraction):
	print (fraction.index(c)+1)
	quit()
print ('-1')