Problem: There is a polyline going through points (0, 0) – (x, x) – (2x, 0) – (3x, x) – (4x, 0) – ... - (2kx, 0) – (2kx + x, x) – .... 

We know that the polyline passes through the point (a, b). Find minimum positive value x such that it is true or determine that there is no such x.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. If there is no such x then output  - 1 as the answer.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

You can see following graphs for sample 1 and sample 3. 

<image> <image>

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

/**
 * Created by Muhamedgarif on 16.09.15.
 */

public class main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int a = scanner.nextInt(), b = scanner.nextInt(), k;
        double[] c = new double[2];
        double res = 2000000000, x;
        c[0] = a - b;
        c[1] = a + b;

        for (int i = 0; i < 2; i++) {
            k = (int) (c[i] / (2 * b));
            if (k != 0) {
                x = c[i] / (2 * k);
                if (x >= b && x < res) {
                    res = x;
                }
            }
        }
        if (res > 1500000000) {
            System.out.print(-1);
        } else {
            System.out.print(res);
        }
    }
}