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.*;
import java.util.Scanner;

import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.FileNotFoundException;

import java.math.BigDecimal;
import java.math.BigInteger;

import java.util.ArrayList;
import java.util.Vector;
import javax.management.StringValueExp;

public class Main {
	public static void main(String[] args) {
	    InputStream inputStream = System.in;
	    OutputStream outputStream = System.out;
	    InputReader in = new InputReader(inputStream);
	    PrintWriter out = new PrintWriter(outputStream);
	    Scanner sc;
	    sc = new Scanner(inputStream);
	    Task solver = new Task();
	    solver.solve(sc, out);
	    out.close();
	}
}

class Task {
	public void solve(Scanner in, PrintWriter out) {
            int n = in.nextInt(), left = in.nextInt();
            int[] a = new int[n];
            int sum = 0;
            for (int i =0; i < n; ++i) {
                a[i] = in.nextInt();
                sum += a[i];
            }

            double middle = 1.0*(sum + left)/n;
            boolean ok = true;
            for (int i = 0; i < n && ok; ++i)
                if (a[i] > middle)
                    ok = false;
            if (!ok)
                out.println(-1);
            else {
                for (int i = 0; i < n; ++i)
                    out.println(middle - a[i]);
            }
        }

}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
}