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;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.PrintStream;
import java.util.Comparator;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.text.NumberFormat;
import java.io.InputStream;
import java.text.DecimalFormat;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author @zhendeaini6001
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {

    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int n = in.nextInt();
        int b = in.nextInt();
        int[] input = IOUtils.readIntArray(in, n);

        int max = 0;
        for (int i = 0;i < n; ++i){
            max = Math.max(max, input[i]);
        }

        long total = ArrayUtils.sumArray(input);

        total += b;

        double av = ((double)total) / n;

        if (av + DoubleUtils.EPS < max){
            out.println(-1);
            return;
        }else{
            for (int i = 0; i < n; ++i){
                double t = av - input[i];
                DoubleUtils.outputWithN(t, 6);
            }
            return;
        }

    }
}

class IOUtils {

    public static int[] readIntArray(Scanner in, int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++)
            array[i] = in.nextInt();
        return array;
    }

    }

class ArrayUtils {

    public static long sumArray(int[] array) {
        long result = 0;
        for (int element : array)
            result += element;
        return result;
    }

    }

class DoubleUtils {
    public static double EPS = 1e-10;

    public static void outputWithN(double res, int n){
        StringBuilder sb = new StringBuilder("0.");
        for (int i = 0; i < n; ++i){
            sb.append("0");
        }
        DecimalFormat df = new DecimalFormat(sb.toString());
        String num = df.format(res);
        System.out.println(num);
    }
}