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. 
n, m, r = [int(x) for x in input().split()]
c = 0
k = 0
for i in range(500):
    c += 1
    n *= 10
    d = n//m
    d = d % 10
    if d == r:
        k = 1
        print(c)
        break
if k == 0:
    print('-1')

 	 	 			 	   			    	  			 			