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.File;
import java.io.FileNotFoundException;
import java.text.DecimalFormat;
import java.util.Arrays;
import java.util.Scanner;

public class ProblemAboutEquation {

    /**
     * @param args
     * @throws FileNotFoundException 
     */
    public static void main(String[] args) throws FileNotFoundException {
        // TODO Auto-generated method stub
        Scanner s = new Scanner(System.in);
        DecimalFormat df = new DecimalFormat("###0.000000");
        int n = s.nextInt();
        
        int bottle = s.nextInt();
        int[] mug = new int[n];
        
        
                
        for (int i = 0; i < mug.length; i++) {
            mug[i] = s.nextInt();
        }
        
        //Arrays.sort(mug);
        
        int highest = findMax(mug);
        double[] addCount = new double[n];
        for (int i = mug.length-1; i >= 0; i--) {
            
            while(mug[i]!=highest){
                mug[i]++;
                addCount[i]++;
                bottle--;
            }
            if(bottle < 0) {
                System.out.println("-1");
                break;
            }
        }
        
        if(!(bottle < 0)) {
        double addLast = (double)bottle / n;
        //System.out.println(addLast);
        for (int i = 0; i < addCount.length; i++) {
            addCount[i] += addLast;
        }
        
        
        for (int i = 0; i < mug.length; i++) {
            System.out.println(df.format(addCount[i]));
            //System.out.println(addCount[i]);
        }
        }
    }

    private static int findMax(int[] mug) {
        // TODO Auto-generated method stub
        int max = 0;
        for (int i = 0; i < mug.length; i++) {
            if(mug[i] > max) max = mug[i];
        }
        
        
        return max;
    }

}