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.*;
import java.security.SecureRandom;
import java.util.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
    
    
	
	
	public void solve() throws Exception {
		int n = sc.nextInt();
		int b = sc.nextInt();
		int a[] = new int[n];
		double s = b;
		for (int i = 0;i < n; ++ i) {
			a[i] = sc.nextInt();
			s += a[i];
		}
		double x = s / (n + 0.0);
		for (int i = 0;i < n; ++ i) {
			if ((double)a[i] - x > 1e-8) {
				out.println(-1);
				return;
			}
		}
		for (int i = 0;i < n; ++ i) {
			out.printf(Locale.US, "%.6f\n", x - a[i]);
		}
    }
    
    
    
    
    /*--------------------------------------------------------------*/
    
    static String filename = "";
    static boolean fromFile = false;
    
    BufferedReader in;
    PrintWriter out;
    FastScanner sc;
    
    public static void main(String[] args) {
        new Thread(null, new Solution(), "", 1 << 25).start();
    }
   
    public void run() {
        try {
            init();
            solve();
        } catch (Exception e) {
            throw new RuntimeException(e);
        } finally {
            out.close();
        }
    }
    
    void init() throws Exception {
    	if (fromFile) {
    		in = new BufferedReader(new FileReader(filename+".in"));
        	out = new PrintWriter(new FileWriter(filename+".out"));
    	} else {
    		in = new BufferedReader(new InputStreamReader(System.in));
        	out = new PrintWriter(System.out);
    	}
        sc = new FastScanner(in);
    }
}

class FastScanner {
    
    BufferedReader reader;
    StringTokenizer strTok;
    
    public FastScanner(BufferedReader reader) {
        this.reader = reader;
    }
    
    public String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            strTok = new StringTokenizer(reader.readLine());
        }
        
        return strTok.nextToken();
    }
    
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    
    public BigInteger nextBigInteger() throws IOException {
    	return new BigInteger(nextToken());
    }
    
    public BigDecimal nextBigDecimal() throws IOException {
    	return new BigDecimal(nextToken());
    }
}