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. 
from decimal import *
a, b, c = map(int, input().split())
getcontext().prec = 100000
dec = Decimal(a) / Decimal(b)
t = -1
s = str(dec)
y = -1
for i in range(100000):
	st = "0"
	if (i < len(s)):
		st = s[i]
	if st == ".":
		y = i
	if st == str(c):
		if y >= 0:
			t = i - y
			break
print(t)