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. 


def main():
	
	a,b,c = map(int, input().split())

	a -= (a//b) * b;

	for i in range(1,1000000):
		a *= 10
		quo = a // b
		if quo == c:
			print(i)
			exit()
		a -= quo * b;
	
	print(-1)
	
	return(0)

main()
