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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution {
    static final int oo = 2 * 1000 * 1000 * 1000;
    static final int B7 = 1000 * 1000 * 1000 + 7;
    static StringTokenizer st = null;
    static final double eps = 1e-9;

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        double b = Double.parseDouble(st.nextToken());

        double[] a = new double[n];

        st = new StringTokenizer(in.readLine());
        double sum = 0.;
        for (int i = 0; i < n; i++) {
            a[i] = Double.parseDouble(st.nextToken());
            sum += a[i];
        }
        double[] c = new double[n];
        double m = (sum + b) / n;

        boolean sol = true;

        for (int i = 0; i < n; i++)
            if (a[i] - m > eps) {
                sol = false;
                break;
            } else
                c[i] = m - a[i];

        if (!sol)
            out.println(-1);
        else
            for (int i = 0; i < n; i++)
                out.printf("%.7f\n", c[i]);

        out.close();
    }
}