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 {
    public static final Reader reader = new InputStreamReader(System.in);
    public static final Writer writer = new OutputStreamWriter(System.out);
    public static final BufferedReader br = new BufferedReader(reader);
    public static final StreamTokenizer st = new StreamTokenizer(br);
    public static final PrintWriter pw = new PrintWriter(writer);
    public static int nextInt() throws IOException {
        st.nextToken();
        return (int)(st.nval);
    }
    
    public static void main(String[] args) throws IOException {
        int n = nextInt();
        int b = nextInt();
        int[] a = new int[n];
        int max = 0;
        int sum = 0;
        for (int i = 0; i < n; ++i) {
            a[i] = nextInt();
            sum += a[i];
            if (a[i] > max) {
                max = a[i];
            }
        }
        int need = max * n - sum;
        if (need > b) {
            pw.println("-1");
            pw.flush();
            return;
        }
        int left = b - need;
        double every = (double)(left) / (double)(n);
        for (int i = 0; i < n; ++i) {
            pw.printf("%.6f\n", (double)(max - a[i]) + every);
        }
        pw.flush();
    }
}