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. 
R = lambda:map(int,raw_input().split())

a,b,c = R()

m = b*[0]
a = a%b
for i in xrange(10000):
    a*=10
    x = a//b  
    if x == c:
	print i+1
	exit(0)
    a = a%b
    if m[a]:
	break 
    m[a] = 1


print -1
