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. 
# force900B


a,b,c = map(int, raw_input().split());


temp = b;
p2 = 0;
p5 = 0;
while temp % 2 == 0:
	p2 += 1;
	temp = temp / 2;

while temp % 5 == 0:
	p5 += 1;
	temp = temp / 5;

times = max(p2, p5) + temp;

res = -1;
i = 1;
while times > 0:
	q = a*10/b;
	if q == c:
		res = i;
		break;
	a = a*10%b;
	i += 1;
	times -= 1;

print res

