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.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.Locale;

public class A {

    public static void main(String[] args) throws Exception {
        int n = nextInt(), b = nextInt();
        int[] a = new int[n];
        
        int sum = b;
        for(int i = 0; i<n; i++) {
            a[i] = nextInt();
            sum += a[i];
        }
        
        double need = sum / (double)n;
        
        for(int i = 0; i<n; i++) {
            if(a[i] > need) {
                exit(-1);
            }
        }
        
        for(int i = 0; i<n; i++) {
            double dd = (need - a[i]);
            String d = String.format("%.6f", dd);
            int ind = d.lastIndexOf('.');
            String s = d.substring(0, ind) + "." + d.substring(ind+1, d.length());
            out.println(s);
        }
        out.flush();
    }

    // ///////////////////////////////////////////////////////////////
    // IO
    // ///////////////////////////////////////////////////////////////
    private static StreamTokenizer in;
    private static PrintWriter out;
    private static BufferedReader inB;

    private static boolean FILE = false;

    private static int nextInt() throws Exception {
        in.nextToken();
        return (int) in.nval;
    }

    private static String nextString() throws Exception {
        in.nextToken();
        return in.sval;
    }

    static {
        try {
            out = new PrintWriter(false ? (new FileOutputStream("out.txt"))
                    : System.out);
            inB = new BufferedReader(new InputStreamReader(
                    FILE ? new FileInputStream("lvl3.txt") : System.in));
        } catch (Exception e) {
            e.printStackTrace();
        }
        in = new StreamTokenizer(inB);
    }

    // ///////////////////////////////////////////////////////////////

    // ///////////////////////////////////////////////////////////////
    // pre - written
    // ///////////////////////////////////////////////////////////////
    private static void println(Object o) throws Exception {
        out.println(o);
        out.flush();
    }

    private static void exit(Object o) throws Exception {
        println(o);
        exit();
    }

    private static void exit() {
        System.exit(0);
    }

    private static final int INF = Integer.MAX_VALUE;
    private static final int MINF = Integer.MIN_VALUE;
    // ////////////////////////////////////////////////////////////////
}