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())
# from random import randrange
# for i in range(50000):
# a, b, c = randrange(1, 10), randrange(1, 100000), randrange(10)


s = set()
ans = ""
while (1):
	if (a in s):
		break
	elif (a == 0): 
		ans += "0"
		break
	elif (a < b):
		s.add(a)
		a *= 10
		ans += "0"
	else:
		s.add(a)
		ans += str(a // b)
		a %= b
		a *= 10
c = str(c)
ans = "." + ans[1:]
# print(ans)
if c not in ans:
	print(-1)
else:
	print(ans.index(c))