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 = 200000
[a, b, c] = list(map(int, input().split()))

q = b
while(q%2==0):
	q//=2
while(q%5==0):
	q//=5

ans = Decimal(a)/Decimal(b)
x = str(ans)
y = -1
p = 0
f = 0
g = 0
for u in x:
	if (f == 1):
		if (int(u) == c):
			y = p
			break
		p += 1
		if (p == b+1):
			g = 1
			break
	if (u == '.'):
		p = 1
		f = 1

if (c == 0):
	if (q == 1 and g == 0):
		y = p
print(y)