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. 
import math as m
MAX=10e5

a,b,c=[int(i) for i in input().split()]
i=0
for i in range(1,int(MAX)):
	d=m.modf(a*10/b)[1]
	if(d==c):
		break
	a=a*10%b
print(i if (i!=MAX-1) else -1)
			   	 	   	  					 		  		 		