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:
/**
     * Created by IntelliJ IDEA.
     * User: SONY
     * Date: 08.04.12
     * Time: 17:55
     * To change this template use File | Settings | File Templates.
     */
    
    import java.io.*;
    import java.util.StringTokenizer;
    
    public class TaskA extends Thread {
        public TaskA(String inputFileName, String outputFileName) {
            try {
                if (inputFileName != null) {
                    this.input = new BufferedReader(new FileReader(inputFileName));
                } else {
                    this.input = new BufferedReader(new InputStreamReader(System.in));
                }
                if (outputFileName != null) {
                    this.output = new PrintWriter(outputFileName);
                } else {
                    this.output = new PrintWriter(System.out);
                }
                this.setPriority(Thread.MAX_PRIORITY);
            } catch (Throwable e) {
                System.err.println(e.getMessage());
                e.printStackTrace();
                System.exit(666);
            }
        }
    
        private void solve() throws Throwable {
            int n = nextInt();
            double b = nextDouble();
            double []a = new double[n];
            for (int i = 0; i < n; ++i) a[i] = nextDouble();
            double max = 0;
            double []ans = new double[n];
            for (double t : a) max = Math.max(t, max);
            for (int i = 0; i < n; ++i) {
                ans[i] += max - a[i];
                b -= ans[i];
                a[i] = max;
            }
            if (b < 0) {
                output.println(-1);
            } else {
                for (int i = 0; i < n; ++i) {
                    output.print((ans[i] + b / n) + " ");
                }
            }
        }
    
        public void run() {
            try {
                solve();
            } catch (Throwable e) {
                System.err.println(e.getMessage());
                e.printStackTrace();
                System.exit(666);
            } finally {
                output.close();
            }
        }
    
        public static void main(String... args) {
            new TaskA(null, null).start();
        }
    
        private int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
    
        private double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    
        private long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    
        private String next() throws IOException {
            while (tokens == null || !tokens.hasMoreTokens()) {
                tokens = new StringTokenizer(input.readLine());
            }
            return tokens.nextToken();
        }
    
        private StringTokenizer tokens;
        private BufferedReader input;
        private PrintWriter output;
    }