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 java.util.Scanner;

public class b {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long A = in.nextLong();
		long B = in.nextLong();
		char C = in.next().charAt(0);
		
		String div = longDivide(A, B);
//		System.out.println(div);
		int i;
		for(i = 0; i < div.length(); i++){
			if(div.charAt(i) == C){
				break;
			}
		}
		if(i == div.length()){
			System.out.println(-1);
			return;
		}
		
		System.out.println(i+1);
	}
	
	static String longDivide(long a, long b){
		long quot = a / b;
		long sub = a;
		StringBuilder sb = new StringBuilder();
		
		while(sb.length() < 100_009){ // or broken
			long mult = quot * b;
			sub = sub - mult;
			
			if(sub == 0){
				sb.append('0');
				return sb.toString();
			}
			
			int pad = 0;
			while(sub / b < 1){
				sub *= 10;
				pad++;
			}
			
			quot = sub / b;
			String str = ""+quot;
//			System.out.println(str);
			pad -= str.length();
			while(pad-->0){
				sb.append('0');
			}
			
			sb.append(str);
			
		}
		
		return sb.toString();
	}
	
}
