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 ProblemAboutEquation {

    public static void main(String args[]) {

        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);

        int tc, i, j;
        String s;
        char p;

        tc = 1;
        while (tc-- > 0) {
            int n = sc.nextInt();
            int k=sc.nextInt();
            int arr[] = sc.readArray(n);
            double sum=k;

            for (i = 0; i < n; i++)
                sum+=arr[i];

            double avg=sum/n;
            boolean flag=false;
            double ans[]=new double[n];

            for (i = 0; i < n; i++) {
                if (arr[i]>avg){
                    flag=true;
                    break;
                }
               else
                   ans[i]=avg-arr[i];
            }

            if (flag)
                out.println(-1);
            else
                for (double item :ans) {
                    System.out.printf("%.6f", item);
                    System.out.println();
                }
        }
        out.close();
    }


    /*
		FASTREADER
	*/
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        /*DEFINED BY ME*/

        //READING ARRAY
        int[] readArray(int n) {
            int arr[] = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }

        //COLLECTIONS SORT
        void sort(int arr[]) {
            ArrayList<Integer> l = new ArrayList<>();
            for (int i : arr)
                l.add(i);
            Collections.sort(l);
            for (int i = 0; i < arr.length; i++)
                arr[i] = l.get(i);
        }

        //EUCLID'S GCD
        int gcd(int a, int b) {
            if (b != 0)
                return gcd(b, a % b);
            else
                return a;
        }
    }
}