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:
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Gaurav
 */import java.io.*;import java.util.*;
public class a174 {
    public static void main(String arg[])throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));


           String a=br.readLine();int large=0,sum=0;
           StringTokenizer s1=new StringTokenizer(a);
           int n=Integer.parseInt(s1.nextToken());
           int m=Integer.parseInt(s1.nextToken());
           int a1[]=new int[n];

           String x=br.readLine();

           StringTokenizer x1=new StringTokenizer(x);

           for(int i=0;i<n;i++)
           {
               a1[i]=Integer.parseInt(x1.nextToken());
               if(a1[i]>large)
                   large=a1[i];
           }
           for(int i=0;i<n;i++)
           {
               a1[i] = Math.abs(a1[i] - large);
               sum=sum+(a1[i]);
        }
         double   y=0.000000;
         y=(m-sum)/(double)n;
         if(y>=0)
         {
             for(int i=0;i<n;i++)
           {
               System.out.printf("%.6f%n",(y+(double)a1[i]));
        }

         }
 else
         {
             System.out.println("-1");
 }

}
}