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.IOException;
import java.io.InputStreamReader;
import java.text.DecimalFormat;
import java.util.StringTokenizer;

public class Main {

	/**
	 * @param args
	 * @throws IOException
	 * @throws NumberFormatException
	 */
	public static void main(String[] args) throws NumberFormatException, IOException {
		new Main().run();
	}

	private StringTokenizer input;
	private BufferedReader reader;
	
	private void run() throws NumberFormatException, IOException {
		openInput(null);

		int n = nextInt();
		int b = nextInt();
		
		int[] a = new int[n];
		int[] d = new int[n];
		int mx = Integer.MIN_VALUE;
		int mn = Integer.MAX_VALUE;
		
		for (int i = 0; i < n; i++) {
			int ai = nextInt();
			a[i] = ai;
			mx = Math.max(mx, ai);
			mn = Math.min(mn, ai);
		}
		
		int total = 0;
		for (int i = 0; i < n; i++) {
			d[i] = mx - a[i];
			total += d[i];
		}
		
		StringBuilder sb = new StringBuilder();
		if (b < total) {
			sb.append("-1");
		} else {
			double diff = (b - total) / (n + 0.0);
			DecimalFormat df = new DecimalFormat("0.000000");
			
			for (int i = 0; i < n; i++) {
				sb.append(df.format(d[i] + diff)).append("\r\n");
			}
		}
		
		System.out.println(sb.toString());
		
		closeInput();
	}
	
	private void openInput(String fileName) {
		reader = new BufferedReader(new InputStreamReader(System.in));
	}
	
	private void closeInput() {
		try {
			reader.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	private String next() throws IOException {
		while (input == null || !input.hasMoreTokens()) {
			input = new StringTokenizer(reader.readLine());
		}
		return input.nextToken();
	}
	
	@SuppressWarnings("unused")
	private long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}
	
	@SuppressWarnings("unused")
	private int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(next());
	}
	
	@SuppressWarnings("unused")
	private double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}

}