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. 

/*	Basic import definitions	*/
	import java.util.*;

/*	Basic Class definitions*/
	public class B900
	{
		public static void main(String[] args) 
		{
			Scanner sc = new Scanner(System.in);

			int i , j , k ;
			int a,b,c;
                        k=-1;
                        a = sc.nextInt();
                        b = sc.nextInt();
                        c = sc.nextInt();
                        
                        for(i=1 ; i<1000007  ; i++)
                        {
                            a *= 10;
                            k = a/b;
                            if(k==c)
                            {
                                System.out.println(i);
                                return;
                            }
                            a %= b;
                        }
                                                    
                        System.out.println(-1);
		}
	}