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.*;
public class Main {
  public static void main (String [] args){
 double x=0;
    int cnt=0;
  	Scanner in = new Scanner (System.in);

  int n= in.nextInt();
  	  int b = in.nextInt();

  	int array [] = new int [n];
      int sort[] = new int [n];

  	  for(int i=1;i<=n;i++){

  	  int a= in.nextInt();
  	  	array[i-1]=a;
  	  	sort[i-1]=a;

  	  }

  	  Arrays.sort(array);

  	  for(int i=n-2;i>=0;i--){

  	  	  cnt+=array[n-1]-array[i];
  	  }

  	  if(b<cnt)
  	  	System.out.print("-1");

  	  	else if(b>cnt || b==cnt){

  	  	x=((double)b-(double)cnt)/(double)n;

  	  	for(int i=0;i<n;i++){


  	  		System.out.print((array[n-1]- sort[i] + x)+ " ");

  	  	}

  }
  }
}