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.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;

public class Main {
	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter pw;

	public static void main(String[] args) throws IOException	{
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = readInt();
		double amt = readInt();
		double[] go = new double[n];
		double max = 0;
		for(int i = 0; i < n; i++)	{
			go[i] = readDouble();
			max = Math.max(max, go[i]);
		}
		double now = 0;
		double[] ret = new double[n];
		for(int i = 0; i < n; i++)	{
			ret[i] = max-go[i];
			now += ret[i];
		}
		if(now > amt)
			pw.println(-1);
		else	{
			amt -= now;
			for(int i = 0; i < n; i++)
				pw.println(ret[i] + amt/n);
		}
		pw.close();
	}

	public static long readLong() throws IOException	{
		return Long.parseLong(nextToken());
	}
	public static double readDouble() throws IOException	{
		return Double.parseDouble(nextToken());
	}
	public static int readInt() throws IOException	{
		return Integer.parseInt(nextToken());
	}
	public static short readShort() throws IOException	{
		return Short.parseShort(nextToken());
	}
	public static String nextToken() throws IOException	{
		while(st == null || !st.hasMoreTokens())	{
			if(!br.ready())	{
				pw.close();
				System.exit(0);
			}
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}
}