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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Collections;
import java.util.Hashtable;
import java.util.Vector;


public class Main {

    /**
     * @param args
     * @throws IOException 
     */
    public static void main(String[] args) throws IOException {
        // TODO Auto-generated method stub
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        //Scanner in=new Scanner(System.in);
        PrintWriter out=new PrintWriter(System.out);
        String[] inp=in.readLine().split(" ");
        int n=Integer.parseInt(inp[0]);
        int b=Integer.parseInt(inp[1]);
        String[] aS=in.readLine().split(" ");
        Vector<Integer> a=new Vector<Integer>();
        for(int i=0; i<n; i++){
            a.add(Integer.parseInt(aS[i]));
        }
        int max=Collections.max(a);
        int[] cnts=new int[n];
        int count=0;
        for(int i=0; i<n; i++){
            cnts[i]=max-a.get(i);
            count+=cnts[i];
        }
        b-=count;
        if(b<0){
            out.print(-1);
        }
        else{
            double plus=(double)b/n;
            for(int i=0; i<n; i++){
                out.println(cnts[i]+plus);
            }
        }
        out.close();
    }

}