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

public class Task{
	
	static final boolean readFromFile = false;
	static final String fileInputName = "input.txt",
						fileOutputName = "output.txt";
	
	public static void main(String args[]){
		FileInputStream fileInputStream;
		FileOutputStream fileOutputStream;
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		if (readFromFile){
			try{
				fileInputStream = new FileInputStream(new File(fileInputName));
				fileOutputStream = new FileOutputStream(new File(fileOutputName));
			}catch (FileNotFoundException e){
				throw new RuntimeException(e);
			}
		}
		PrintWriter out = new PrintWriter((readFromFile)?fileOutputStream:outputStream);
		InputReader in  = new InputReader((readFromFile)?fileInputStream:inputStream);
		
		Solver s = new Solver(in, out);
		s.solve();
		
		out.close();
	}
}

class Solver{
	private PrintWriter out;
	private InputReader in;
	
	public void solve(){
		int n = in.nextInt(),
				b = in.nextInt(),
				sum = b,
				a[] = new int[n];
		for (int i=0;i<n;i++){
			a[i] = in.nextInt();
			sum += a[i];
		}
		double k = (double)sum/n;
		double A[] = new double[n];
		for (int i=0;i<n;i++){
			A[i] = k-a[i];
			if (A[i]<0){
				out.println("-1");
				return;
			}
		}
		for (int i=0;i<n;i++){
			String ans = Double.toString(A[i]);
			int pos = 0;
			for (int j=1;j<ans.length();j++)
				if (ans.charAt(j)=='.'){
					pos = j;
					break;
				}
			for (int j=0;j<pos+7;j++)
				out.print((j<ans.length())?ans.charAt(j):"0");
			out.println();
		}
	}
	
	Solver(InputReader in, PrintWriter out){
		this.in = in;
		this.out = out;
	}
}

class InputReader{
	StringTokenizer tok;
	BufferedReader buf;
	
	InputReader(InputStream in){
		tok = null;
		buf = new BufferedReader(new InputStreamReader(in));
	}

	InputReader(FileInputStream in){
		tok = null;
		buf = new BufferedReader(new InputStreamReader(in));
	}
	
	public String next(){
		while (tok==null || !tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(buf.readLine());
			}catch (IOException e){
				throw new RuntimeException(e);
			}
		}
		return tok.nextToken();
	}
	
	public int nextInt(){
		return Integer.parseInt(next());
	}
	public long nextLong(){
		return Long.parseLong(next());
	}
	public double nextDouble(){
		return Double.parseDouble(next());
	}
	public float nextFloat(){
		return Float.parseFloat(next());
	}
	public String nextLine(){
		try{
			return buf.readLine();
		}catch (IOException e){
			return null;
		}
	}
	public char nextChar(){
		return next().charAt(0);
	}
}