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 *
getcontext().prec = 2048
getcontext().rounding = ROUND_DOWN

a, b, c = [int(x) for x in input().strip().split(" ")]
if b == 0:
	print(-1)
else:
	strNum = str(Decimal(a)/Decimal(b))
	strNum = [int(x) for x in strNum[strNum.index('.')+1:]]
	try:
		print(strNum.index(c)+1)
	except:
		if c == 0 and len(strNum) != 2048:
			print(len(strNum) + 1)
		else:
			print(-1)