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 = raw_input().split()
b = [int(num) for num in a]


x = b[0]
y = b[1]
z = b[2]

if x == y:
	if z == 0:
		print 0
	else:
		print -1
else:
	p = 1
	d = (x * 10) / y
	x = (x * 10) % y
	per = 1000007
	while per:
		per -= 1
		if z == d:
			print p
			exit()
		d = (x * 10) / y
		x = (x * 10) % y
		p += 1
	print -1
