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. 
x = input().split()
a = int(x[0])
b = int(x[1])
c = int(x[2])

y = (a * (10**10000)) // b
z = a // b;
s = str(y)
ss = str(z)
dif = 10000 - len(s)
for i in range(dif):
	s = '0' + s

if (ss == '0'):
	 ss = ''

for i in range(0, len(s) - len(ss)):
	if (s[i + len(ss)] == str(c)):
		print(i+1)
		exit(0)

print("-1")
