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.PrintWriter;
import java.util.Locale;
import java.util.Scanner;

public class Main {

   Scanner in;
   PrintWriter out;

   // class Scanner {
   // StreamTokenizer in;
   //
   // Scanner(InputStream stream) {
   // in = new StreamTokenizer(new BufferedReader(new
   // InputStreamReader(stream)));
   // in.resetSyntax();
   // in.whitespaceChars(0, 32);
   // in.wordChars(33, 255);
   // }
   //
   // String next() {
   // try {
   // in.nextToken();
   // return in.sval;
   // } catch (Exception e) {
   // throw new Error();
   // }
   // }
   //
   // long nextLong() {
   // return Long.parseLong(next());
   // }
   //
   // int nextInt() {
   // return Integer.parseInt(next());
   // }
   // }

   void asserT(boolean e) {
      if (!e) {
         throw new Error();
      }
   }

   void solve() {
      in.useLocale(Locale.US);
      int n = in.nextInt();
      int b = in.nextInt();
      int max = 0;
      int ar[] = new int[n];
      for (int i =0; i < n; i++ ){
         ar[i] = in.nextInt();
         max = Math.max(max, ar[i]);
      }
      int toEqual = 0;
      for (int i = 0; i < n; i++){
         toEqual+=max-ar[i];
      }
      if (toEqual>b){
         out.println(-1);
         return;
      }
      double delta = b-toEqual;
      double toEvery = delta/n;
      double level = max+toEvery;
      double toUp[] = new double[n];
      for (int i = 0; i < n; i++){
         toUp[i] = level-ar[i];
      }
      for (int i = 0;i <n; i++){
         out.printf(Locale.US, "%7f",toUp[i]);
         out.println();
      }
   }

   void run() {
      in = new Scanner(System.in);
      out = new PrintWriter(System.out);
      try {
         solve();
      } finally {
         out.close();
      }
   }

   public static void main(String[] args) {
      new Main().run();
   }
}