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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.*;


public class Solution {

	public static void main(String[] Args) throws IOException
	{
		new Solution().Run();
	}
	
	BufferedReader Br;
	StreamTokenizer St;
	PrintWriter Pw;
	
	int N;
	int Left;
	int[] Cups;
	int Sum;
	int Max;
	
	
	public void Reading() throws IOException
	{
		St.nextToken();
		N=(int)St.nval;
		St.nextToken();
		Left=(int)St.nval;
		Cups=new int[N];
		Sum=Left;
		Max=0;
		for (int i=0; i<N; i++)
		{
			St.nextToken();
			Cups[i]=(int)St.nval;
			Sum+=Cups[i];
			if (Max<Cups[i])
				Max=Cups[i];
		}
	}
	
	public void Writing()
	{
		if (Sum/N<Max)
			Pw.println("-1");
		else
		{
			double zn=(double)Sum/N;
			for (int i=0; i<N; i++)
			{
				Pw.println(zn-Cups[i]);
			}
		}
	}
	
	public void Run() throws IOException
	{
		File f1=new File("input.txt");
		//Br=new BufferedReader(new FileReader(f1));
		Br=new BufferedReader(new InputStreamReader(System.in));
		St=new StreamTokenizer(Br);
		Reading();
		
		File f2=new File("output.txt");
		//Pw=new PrintWriter(f2);
		Pw=new PrintWriter(new OutputStreamWriter(System.out));
		Writing();
		Pw.flush();
	}
	
}