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.*;
import java.util.*;

public class Main {
  BufferedReader br;
  
  public void go() throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    String s = br.readLine();
    String[] ss = s.split(" ");
    int n = Integer.parseInt(ss[0]);
    int b = Integer.parseInt(ss[1]);
    int[] a = new int[n];
    
    int sum = 0;
    s = br.readLine();
    ss = s.split(" ");
    for (int i = 0; i < n; i++)
      sum += a[i] = Integer.parseInt(ss[i]);
    
    sum += b;
    double each = (double) sum / (double) n;
    
    for (int i = 0; i < n; i++)
      if (a[i] > each) {
        System.out.println("-1");
        return;
      }
    
    for (int i = 0; i < n; i++)
      System.out.println(each - (double) a[i] + 1e-10);
  }
  
  public static void main(String[] args) throws Exception {
    new Main().go();
  }
}