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;
public class ProblemAboutEquation {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n,b;
		double total=0.0,k;
		n=sc.nextInt();
		b=sc.nextInt();
		double arr[] = new double[n+1];
		double ans[] = new double[n+1];
 		for(int i=0;i<n;i++) {
			arr[i]=sc.nextDouble();
			total+=arr[i];
		}
		total = total + (double)(b);
		k=total/(double)(n);
		sc.close();
		for(int i=0;i<n;i++)
		{
			if(arr[i]>k)
			{
				System.out.println(-1);
				return ;
			}
			else
			{
				ans[i]=k-arr[i];
				
			}
		}
		
		for(int i=0;i<n;i++)
			System.out.println(ans[i]);
		
	}
}