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. 
def get_int(string, n):
	i = j = k = 0
	for s in string:
		k += 1
	for s in string:
		if i == n - 1:
			break
		if s == ' ':
			i += 1
		j += 1
	i = 0
	while j < k:
		if string[j] == ' ':
			break
		i = 10 * i + int(string[j])
		j += 1
	return i
	
x = input()
a = get_int(x, 1)
b = get_int(x, 2)
c = get_int(x, 3)
n = -1

for i in range(1, 10000):
	a *= 10
	if (a // b) % 10 == c:
		n = i
		break
	
print(n)