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.math.BigDecimal;
import java.util.Scanner;

public class B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		// 22/7, 333/106 99991

		int a = in.nextInt();
		int b = in.nextInt();
		int c = in.nextInt();

		String temp = Integer.toString(a);
		int[] aArr = new int[temp.length()];
		for (int i = 0; i < temp.length(); i++) {
			aArr[i] = temp.charAt(i) - '0';
		}
		temp = Integer.toString(a);
		int[] bArr = new int[temp.length()];
		for (int i = 0; i < temp.length(); i++) {
			bArr[i] = temp.charAt(i) - '0';
		}

		int len = bArr.length;
		int count = 0;
		int cur = a;
		boolean first = true;
		long t = System.currentTimeMillis();
		while (System.currentTimeMillis() - t < 800) {
			if (cur < b) {
				if (c == 0 && !first) {
					System.out.println(count);
					System.exit(0);
				}
			}
			else {
				int div = cur / b;
				cur = cur % b;
				if (c == div) {
					System.out.println(count);
					System.exit(0);
				}
			}

			count++;
			cur *= 10;
			first = false;
		}
		
		System.out.println(-1);
	}
}
