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. 
import sys
a,b,c = list(map(int, input().split()))

#while a<b:
#	a*=10
a = a % b
a *= 10
steps = 0
for i in range(100000):
	d = a//b
	rem = a-b*(a//b)
	#print('d:', d, 'rem:', rem)
	for id,x in enumerate(str(d)):
		if int(x) == c:
			print(steps + id + 1)
			sys.exit(0)
	steps += len(str(d))
	a = 10*rem
	
print(-1)
