Problem: A group of n merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the n mugs must be the same.

Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has a1 milliliters of the drink, the second one has a2 milliliters and so on. The bottle has b milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.

Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously: 

  * there were b milliliters poured in total. That is, the bottle need to be emptied; 
  * after the process is over, the volumes of the drink in the mugs should be equal. 

Input

The first line contains a pair of integers n, b (2 ≤ n ≤ 100, 1 ≤ b ≤ 100), where n is the total number of friends in the group and b is the current volume of drink in the bottle. The second line contains a sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 100), where ai is the current volume of drink in the i-th mug.

Output

Print a single number "-1" (without the quotes), if there is no solution. Otherwise, print n float numbers c1, c2, ..., cn, where ci is the volume of the drink to add in the i-th mug. Print the numbers with no less than 6 digits after the decimal point, print each ci on a single line. Polycarpus proved that if a solution exists then it is unique.

Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma.

Examples

Input

5 50
1 2 3 4 5


Output

12.000000
11.000000
10.000000
9.000000
8.000000


Input

2 2
1 100


Output

-1

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class BerCola {

    public static void main(String[] args) {

        double aTotal = 0, y = 1, totalAnswer = 0;
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        double b = input.nextDouble();
        String toString;
        double[] as = new double[n];
        double[] answers = new double[n];

        for (int i = 0; i < n; ++i) {
            as[i] = input.nextDouble();
            aTotal += as[i];

        }

        if (n >= 2 && n <= 100 && b >= 1 && b <= 100) {

            for (int i = 0; i < n; i++) {
                if (as[i] >= 0 && as[i] <= 100) {
                    answers[i] = (aTotal + b) / n - as[i];
                    if (as[i] > ((aTotal + b) / n)) {
                        y = 0;
                    }

                }

            }
            if (y == 1) {
                for (int i = 0; i < n; i++) {

                    System.out.printf("%f \n", answers[i]);

                }
            } else {
                System.out.println("-1");
            }

        }
    }

}