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.util.Scanner;
import java.util.Arrays;
public class Ishu
{
	public static void main(String []args)
	{
	Scanner scan=new Scanner(System.in);
	int n,b,i,sum=0,index=0;
	String str;
	double temp;	
	boolean flag=true;
	int[] a=new int[100];
	n=scan.nextInt();
	b=scan.nextInt();
	for(i=0;i<n;++i)
		{
		a[i]=scan.nextInt();
		sum+=a[i];
		}
	sum+=b;	
	temp=(double)sum/n;
	for(i=0;i<n;++i)
		if((double)a[i]>temp)
			{
			System.out.println(-1);
			return;
			}
	for(i=0;i<n;++i)
		{
		str=String.valueOf(temp-a[i]);
		index=str.indexOf('.');
		if(str.length()-index<7)
			{
			while(str.length()-index<7)
				str+="0";
			}
		else if(str.length()-index>7)
			str=String.valueOf(Math.round((temp-a[i])*1000000.0)/1000000.0);
		System.out.println(str);
		}
	}
}