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.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		(new Main()).solve();
	}

	public void Main() {
	}

	void solve() throws IOException {
		// BufferedReader in = new BufferedReader(new
		// InputStreamReader(System.in));
		// Scanner in = new Scanner(System.in);
		MyReader in = new MyReader();
		PrintWriter out = new PrintWriter(System.out);
		// Scanner in = new Scanner(new FileReader("input.txt"));
		// PrintWriter out = new PrintWriter("output.txt");
		int n = in.nextInt();
		int b = in.nextInt();
		int[] a = new int[n];
		int s = 0;
		int max = 0;
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
			s+=a[i];
			if (a[i] > max) {
				max = a[i];
			}
		}
		double d = (0.0 + s + b) / n;
		if (max > d) {
			out.println(-1);
		} else {
			for (int i = 0; i < n; i++) {
				out.print((d - a[i]) + " ");
			}
		}
		
		out.close();
	}

};

class MyReader {
	private BufferedReader in;
	String[] parsed;
	int index = 0;

	public MyReader() {
		in = new BufferedReader(new InputStreamReader(System.in));
	}

	public int nextInt() throws NumberFormatException, IOException {
		if (parsed == null || parsed.length == index) {
			read();
		}
		return Integer.parseInt(parsed[index++]);
	}

	private void read() throws IOException {
		parsed = in.readLine().split(" ");
		index = 0;
	}

	public String readLine() throws IOException {
		return in.readLine();
	}
};